2022
JEE Mains
MCQ
JEE Main 2022 (Online) 26th June Evening Shift
Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 $\mu$C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :
A.
1 : 4
B.
4 : 1
C.
1 : 8
D.
8 : 1
2022
JEE Mains
MCQ
JEE Main 2022 (Online) 26th June Morning Shift
Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : Non-polar materials do not have any permanent dipole moment.
Reason (R) : When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution.
In the light of above statements, choose the most appropriate answer from the options given below.
A.
Both (A) and (R) are correct and (R) is the correct explanation of (A).
B.
Both (A) and (R) are correct and (R) is not the correct explanation of (A).
C.
(A) is correct but (R) is not correct.
D.
(A) is not correct but (R) is correct.
2022
JEE Mains
MCQ
JEE Main 2022 (Online) 25th June Morning Shift
In the figure, a very large plane sheet of positive charge is shown. P1 and P2 are two points at distance l and 2l from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields E1 and E2 at P1 and P2 respectively are :
A.
${E_1} = \sigma /{\varepsilon _0},\,{E_2} = \sigma /2{\varepsilon _0}$
B.
${E_1} = 2\sigma /{\varepsilon _0},\,{E_2} = \sigma /{\varepsilon _0}$
C.
${E_1} = {E_2} = \sigma /2{\varepsilon _0}$
D.
${E_1} = {E_2} = \sigma /{\varepsilon _0}$
2022
JEE Mains
MCQ
JEE Main 2022 (Online) 24th June Evening Shift
Two identical charged particles each having a mass 10 g and charge 2.0 $\times$ 10$-$7C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 ms$-$2]
A.
12 cm
B.
10 cm
C.
8 cm
D.
5 cm
2022
JEE Mains
MCQ
JEE Main 2022 (Online) 24th June Evening Shift
A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :
A.
${{\rho q{R^2}} \over {4{\varepsilon _0}}}$
B.
${{\rho q{R^2}} \over {2{\varepsilon _0}}}$
C.
${{q\rho } \over {4{\varepsilon _0}{R^2}}}$
D.
${{4{\varepsilon _0}{R^2}} \over {q\rho }}$
2022
JEE Mains
MCQ
JEE Main 2022 (Online) 24th June Morning Shift
A vertical electric field of magnitude 4.9 $\times$ 105 N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be :
(Given : g = 9.8 m/s2)
A.
1.6 $\times$ 10$-$9 C
B.
2.0 $\times$ 10$-$9 C
C.
3.2 $\times$ 10$-$9 C
D.
0.5 $\times$ 10$-$9 C
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 1st September Evening Shift
A cube is placed inside an electric field, $\overrightarrow E = 150{y^2}\widehat j$. The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is :
A.
3.8 $\times$ 10$-$11 C
B.
8.3 $\times$ 10$-$11 C
C.
3.8 $\times$ 10$-$12 C
D.
8.3 $\times$ 10$-$12 C
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 31st August Evening Shift
Choose the incorrect statement :
(1) The electric lines of force entering into a Gaussian surface provide negative flux.
(2) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same.
(3) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.
(4) When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux.
Choose the most appropriate answer from the options given below
(1) The electric lines of force entering into a Gaussian surface provide negative flux.
(2) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same.
(3) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.
(4) When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux.
Choose the most appropriate answer from the options given below
A.
(3) and (4) only
B.
(2) and (4) only
C.
(4) only
D.
(1) and (3) only
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 31st August Morning Shift
Two particles A and B having charges 20$\mu$C and $-$5$\mu$C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?
A.
At 5 cm from 20 $\mu$C on the left side of system
B.
At 5 cm from $-$5 $\mu$C on the right side
C.
At 1.25 cm from $-$5 $\mu$C between two charges
D.
At midpoint between two charges
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 27th August Evening Shift
Figure shows a rod AB, which is bent in a 120$^\circ$ circular arc of radius R. A charge ($-$Q) is uniformly distributed over rod AB. What is the electric field $\overrightarrow E $ at the centre of curvature O ?
A.
${{3\sqrt 3 Q} \over {8\pi {\varepsilon _0}{R^2}}}(\widehat i)$
B.
${{3\sqrt 3 Q} \over {8{\pi ^2}{\varepsilon _0}{R^2}}}(\widehat i)$
C.
${{3\sqrt 3 Q} \over {16{\pi ^2}{\varepsilon _0}{R^2}}}(\widehat i)$
D.
${{3\sqrt 3 Q} \over {8{\pi ^2}{\varepsilon _0}{R^2}}}( - \widehat i)$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 27th August Morning Shift
A uniformly charged disc of radius R having surface charge density $\sigma$ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :-
A.
$E = {\sigma \over {2{\varepsilon _0}}}\left( {1 - {Z \over {{{({Z^2} + {R^2})}^{1/2}}}}} \right)$
B.
$E = {\sigma \over {2{\varepsilon _0}}}\left( {1 + {Z \over {{{({Z^2} + {R^2})}^{1/2}}}}} \right)$
C.
$E = {{2{\varepsilon _0}} \over \sigma }\left( {{1 \over {{{({Z^2} + {R^2})}^{1/2}}}} + Z} \right)$
D.
$E = {\sigma \over {2{\varepsilon _0}}}\left( {{1 \over {({Z^2} + {R^2})}} + {1 \over {{Z^2}}}} \right)$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 26th August Evening Shift
The two thin coaxial rings, each of radius 'a' and having charges +Q and $-$Q respectively are separated by a distance of 's'. The potential difference between the centres of the two rings is :
A.
${Q \over {2\pi {\varepsilon _0}}}\left[ {{1 \over a} + {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]$
B.
${Q \over {4\pi {\varepsilon _0}}}\left[ {{1 \over a} + {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]$
C.
${Q \over {4\pi {\varepsilon _0}}}\left[ {{1 \over a} - {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]$
D.
${Q \over {2\pi {\varepsilon _0}}}\left[ {{1 \over a} - {1 \over {\sqrt {{s^2} + {a^2}} }}} \right]$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 26th August Morning Shift
A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in the figure. The approximate variation electric field $\overrightarrow E $ as a function of distance r from centre O is given by
A.
B.
C.
D.
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 27th July Evening Shift
What will be the magnitude of electric field at point O as shown in the figure? Each side of the figure is l and perpendicular to each other?
A.
${1 \over {4\pi {\varepsilon _0}}}{q \over {{l^2}}}$
B.
${1 \over {4\pi {\varepsilon _0}}}{q \over {(2{l^2})}}\left( {2\sqrt 2 - 1} \right)$
C.
${q \over {4\pi {\varepsilon _0}{{(2l)}^2}}}$
D.
${1 \over {4\pi {\varepsilon _0}}}{{2q} \over {2{l^2}}}\left( {\sqrt 2 } \right)$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 27th July Morning Shift
Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '$\theta$' with the vertical?
A.
$x = {\left( {{{{q^2}l} \over {2\pi {\varepsilon _0}mg}}} \right)^{{1 \over 2}}}$
B.
$x = {\left( {{{{q^2}l} \over {2\pi {\varepsilon _0}mg}}} \right)^{{1 \over 3}}}$
C.
$x = {\left( {{{{q^2}{l^2}} \over {2\pi {\varepsilon _0}{m^2}g}}} \right)^{{1 \over 3}}}$
D.
$x = {\left( {{{{q^2}{l^2}} \over {2\pi {\varepsilon _0}{m^2}{g^2}}}} \right)^{{1 \over 3}}}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 25th July Evening Shift
Two ideal electric dipoles A and B, having their dipole moment p1 and p2 respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37$^\circ$ with the axis. The ratio of the dipole moment of A and B, ${{{p_1}} \over {{p_2}}}$ is : (take $\sin 37^\circ = {3 \over 5}$)
A.
${3 \over 8}$
B.
${3 \over 2}$
C.
${2 \over 3}$
D.
${4 \over 3}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 22th July Evening Shift
An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 $\times$ 10$-$6 C/m. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.
A.
0.485 mC
B.
815.1 nC
C.
8.8 $\mu$C
D.
4.44 $\mu$C
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 20th July Morning Shift
A certain charge Q is divided into two parts q and (Q $-$ q). How should the charges Q and q be divided so that q and (Q $-$ q) placed at a certain distance apart experience maximum electrostatic repulsion?
A.
Q = 2q
B.
Q = 4q
C.
Q = 3q
D.
Q = ${q \over 2}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 18th March Morning Shift
An oil drop of radius 2 mm with a density 3g cm$-$3 is held stationary under a constant electric field 3.55 $\times$ 105 V m$-$1 in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider g = 9.81 m/s2)
A.
48.8 $\times$ 1011
B.
1.73 $\times$ 1010
C.
17.3 $\times$ 1010
D.
1.73 $\times$ 1012
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 16th March Evening Shift
Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the z-axis in free space.
A.
0.424 nC m$-$2
B.
4.0 nC m$-$2
C.
47.88 C/m
D.
0.07 nC m$-$2
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 26th February Evening Shift
Given below are two statements:
Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.
Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (< R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero..
In the light of the above statements, choose the correct answer from the options given below :
Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.
Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (< R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero..
In the light of the above statements, choose the correct answer from the options given below :
A.
Both Statement I and Statement II are true
B.
Statement I is false but Statement II is true
C.
Statement I is true but Statement II is false
D.
Both Statement I and Statement II are false
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 26th February Evening Shift
An inclined plane making an angle of 30$^\circ$ with the horizontal is placed in a uniform horizontal electric field $200{N \over C}$ as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.
[g = 9.8 m/s2; $\sin 30^\circ = {1 \over 2}$; $\cos 30^\circ = {{\sqrt 3 } \over 2}$]
[g = 9.8 m/s2; $\sin 30^\circ = {1 \over 2}$; $\cos 30^\circ = {{\sqrt 3 } \over 2}$]
A.
0.46 s
B.
0.92 s
C.
1.3 s
D.
2.3 s
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 26th February Morning Shift
Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = ${{\sqrt 3 } \over 2}L$.
A.
${Q \over {4\pi {\varepsilon _0}{L^2}}}$
B.
${Q \over {3\pi {\varepsilon _0}{L^2}}}$
C.
${Q \over {2\sqrt 3 \pi {\varepsilon _0}{L^2}}}$
D.
${{\sqrt 3 Q} \over {4\pi {\varepsilon _0}{L^2}}}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 25th February Evening Shift
A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\overrightarrow E $ through the shaded area is :
A.
${q \over {24{\varepsilon _0}}}$
B.
${q \over {48{\varepsilon _0}}}$
C.
${q \over {4{\varepsilon _0}}}$
D.
${q \over {8{\varepsilon _0}}}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 24th February Evening Shift
Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : (m = mass of charged particle)
A.
${\left( {{{2{q^2}} \over {\pi {\varepsilon _0}m{d^3}}}} \right)^{{1 \over 2}}}$
B.
${\left( {{{{q^2}} \over {2\pi {\varepsilon _0}m{d^3}}}} \right)^{{1 \over 2}}}$
C.
${\left( {{{2\pi {\varepsilon _0}m{d^3}} \over {{q^2}}}} \right)^{{1 \over 2}}}$
D.
${\left( {{{\pi {\varepsilon _0}m{d^3}} \over {2{q^2}}}} \right)^{{1 \over 2}}}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 24th February Morning Shift
A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is $-$Q. The electric field at the centre of cube is :
A.
${{2Q} \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)$
B.
${{ - Q} \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)$
C.
${Q \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)$
D.
${{ - 2Q} \over {3\sqrt 3 \pi {\varepsilon _0}{a^2}}}\left( {\widehat x + \widehat y + \widehat z} \right)$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Evening Slot
Two identical electric point dipoles have dipole moments ${\overrightarrow p _1} = p\widehat i$ and ${\overrightarrow p _2} = - p\widehat i$ and are held on the x
axis at distance '$a$' from each other. When released, they move along the x-axis with the direction
of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when
they are infinitely far apart is :
A.
${p \over a}\sqrt {{3 \over {2\pi { \in _0}ma}}} $
B.
${p \over a}\sqrt {{1 \over {\pi { \in _0}ma}}} $
C.
${p \over a}\sqrt {{1 \over {2\pi { \in _0}ma}}} $
D.
${p \over a}\sqrt {{2 \over {\pi { \in _0}ma}}} $
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Evening Slot
Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying
charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is
placed at distance r from the centre of the shell?
A.
${1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{R^2}}} > F > 0$ for r < R
B.
$F = {1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{r^2}}}$ for r > R
C.
$F = {1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{r^2}}}$ for all r
D.
$F = {1 \over {4\pi {\varepsilon _0}}}{{qQ} \over {{R^2}}}$ for r < R
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Morning Slot
Charges Q1
and Q2
are at points A and B of a right angle triangle OAB (see figure). The resultant
electric field at point O is perpendicular to the hypotenuse, then
${{{Q_1}} \over {{Q_2}}}$ is proportional to :
${{{Q_1}} \over {{Q_2}}}$ is proportional to :
A.
${{x_1^3} \over {x_2^3}}$
B.
${{x_2^2} \over {x_1^2}}$
C.
${{{x_1}} \over {{x_2}}}$
D.
${{{x_2}} \over {{x_1}}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 5th September Evening Slot
Ten charges are placed on the circumference
of a circle of radius R with constant angular
separation between successive charges.
Alternate charges 1, 3, 5, 7, 9 have charge (+q)
each, while 2, 4, 6, 8, 10 have charge (–q) each.
The potential V and the electric field E at the
centre of the circle are respectively.
(Take V = 0 at infinity)
(Take V = 0 at infinity)
A.
V = 0; E = 0
B.
$V = {{10q} \over {4\pi {\varepsilon _0}R}}$; $E = {{10q} \over {4\pi {\varepsilon _0}{R^2}}}$
C.
$V = {{10q} \over {4\pi {\varepsilon _0}R}}$; E = 0
D.
V = 0; $E = {{10q} \over {4\pi {\varepsilon _0}{R^2}}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 5th September Morning Slot
A solid sphere of radius R carries a charge
Q + q distributed uniformly over its volume. A
very small point like piece of it of mass m gets
detached from the bottom of the sphere and
falls down vertically under gravity. This piece
carries charge q. If it acquires a speed v when
it has fallen through a vertical height y (see
figure), then :
(assume the remaining portion to be spherical).
(assume the remaining portion to be spherical).
A.
v2 = $y\left[ {{{qQ} \over {4\pi {\varepsilon _0}R\left( {R + y} \right)m}} + g} \right]$
B.
v2 = $2y\left[ {{{qQR} \over {4\pi {\varepsilon _0}{{\left( {R + y} \right)}^3}m}} + g} \right]$
C.
v2 = $2y\left[ {{{qQ} \over {4\pi {\varepsilon _0}R\left( {R + y} \right)m}} + g} \right]$
D.
v2 = $y\left[ {{{qQ} \over {4\pi {\varepsilon _0}{R^2}ym}} + g} \right]$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 4th September Evening Slot
A particle of charge q and mass m is subjected to an electric field
E = E0 (1 – $a$x2) in the x-direction, where $a$ and E0 are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :
E = E0 (1 – $a$x2) in the x-direction, where $a$ and E0 are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :
A.
$a$
B.
$\sqrt {{2 \over a}} $
C.
$\sqrt {{3 \over a}} $
D.
$\sqrt {{1 \over a}} $
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 4th September Morning Slot
Two charged thin infinite plane sheets of
uniform surface charge density ${\sigma _ + }$ and ${\sigma _ - }$,
where |${\sigma _ + }$| > |${\sigma _ - }$|, intersect at right angle.
Which of the following best represents the
electric field lines for this system :
uniform surface charge density ${\sigma _ + }$ and ${\sigma _ - }$,
where |${\sigma _ + }$| > |${\sigma _ - }$|, intersect at right angle.
Which of the following best represents the
electric field lines for this system :
A.
B.
C.
D.
Given, |${\sigma _ + }$| > |${\sigma _ - }$|
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 4th September Morning Slot
A two point charges 4q and -q are fixed
on the x-axis at x = $ - {d \over 2}$
and x = ${d \over 2}$
respectively. If a third point charge 'q' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will :
A.
increase by ${{3{q^2}} \over {4\pi {\varepsilon _0}d}}$
B.
increase by ${{2{q^2}} \over {3\pi {\varepsilon _0}d}}$
C.
decrease by ${{{q^2}} \over {4\pi {\varepsilon _0}d}}$
D.
decrease by ${{4{q^2}} \over {3\pi {\varepsilon _0}d}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 3rd September Evening Slot
Concentric metallic hollow spheres of radii R and 4R hold charges Q1
and Q2
respectively. Given that
surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :
A.
${{3{Q_2}} \over {4\pi {\varepsilon _0}R}}$
B.
${{3{Q_1}} \over {4\pi {\varepsilon _0}R}}$
C.
${{3{Q_1}} \over {16\pi {\varepsilon _0}R}}$
D.
${{{Q_2}} \over {4\pi {\varepsilon _0}R}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 3rd September Morning Slot
Two isolated conducting spheres S1 and S2 of
radius ${2 \over 3}R$ and ${1 \over 3}R$ have 12 $\mu $C and –3 $\mu $C
charges, respectively, and are at a large
distance from each other. They are now
connected by a conducting wire. A long time
after this is done the charges on S1 and S2 are
respectively :
A.
4.5 $\mu $C on both
B.
+4.5 $\mu $C and –4.5 $\mu $C
C.
6 $\mu $C and 3 $\mu $C
D.
3 $\mu $C and 6 $\mu $C
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 2nd September Evening Slot
A small point mass carrying some positive
charge on it, is released from the edge of a
table. There is a uniform electric field in this
region in the horizontal direction. Which of the
following options then correctly describe the
trajectory of the mass?
(Curves are drawn schematically and are not to scale).
(Curves are drawn schematically and are not to scale).
A.
B.
C.
D.
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 2nd September Evening Slot
A charge Q is distributed over two concentric
conducting thin spherical shells radii r and
R (R > r). If the surface charge densities on the
two shells are equal, the electric potential at
the common centre is :
A.
${1 \over {4\pi {\varepsilon _0}}}{{\left( {R + r} \right)} \over {\left( {{R^2} + {r^2}} \right)}}$Q
B.
${1 \over {4\pi {\varepsilon _0}}}{{\left( {R + r} \right)} \over {2\left( {{R^2} + {r^2}} \right)}}Q$
C.
${1 \over {4\pi {\varepsilon _0}}}{{\left( {R + 2r} \right)Q} \over {2\left( {{R^2} + {r^2}} \right)}}$
D.
${1 \over {4\pi {\varepsilon _0}}}{{\left( {2R + r} \right)} \over {\left( {{R^2} + {r^2}} \right)}}Q$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 2nd September Morning Slot
A charged particle (mass m and charge q)
moves along X-axis with velocity V0. When it
passes through the origin it enters a region having uniform electric field
$\overrightarrow E = - E\widehat j$ which extends upto x = d.
Equation of path of electron in the region x > d is
moves along X-axis with velocity V0. When it
passes through the origin it enters a region having uniform electric field
$\overrightarrow E = - E\widehat j$ which extends upto x = d.
Equation of path of electron in the region x > d is
A.
y = ${{qEd} \over {mV_0^2}}\left( {x - d} \right)$
B.
y = ${{qEd} \over {mV_0^2}}\left( {{d \over 2} - x} \right)$
C.
y = ${{qEd} \over {mV_0^2}}x$
D.
y = ${{qE{d^2}} \over {mV_0^2}}x$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 9th January Morning Slot
Consider a sphere of radius R which carries a
uniform charge density $\rho $. If a sphere of radius ${{R \over 2}}$ is carved out of it, as shown, the ratio ${{\left| {\overrightarrow {{E_A}} } \right|} \over {\left| {\overrightarrow {{E_B}} } \right|}}$ of magnitude of electric field ${\overrightarrow {{E_A}} }$ and ${\overrightarrow {{E_B}} }$,
respectively, at points A and B due to the
remaining portion is :
A.
${{17} \over {54}}$
B.
${{18} \over {54}}$
C.
${{18} \over {34}}$
D.
${{21} \over {34}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 9th January Morning Slot
An electric dipole of moment
$\overrightarrow p = \left( { - \widehat i - 3\widehat j + 2\widehat k} \right) \times {10^{ - 29}} $ C.m is
at the origin (0, 0, 0). The electric field due to this dipole at
$\overrightarrow r = + \widehat i + 3\widehat j + 5\widehat k$ (note that $\overrightarrow r .\overrightarrow p = 0$ ) is parallel to :
$\overrightarrow p = \left( { - \widehat i - 3\widehat j + 2\widehat k} \right) \times {10^{ - 29}} $ C.m is
at the origin (0, 0, 0). The electric field due to this dipole at
$\overrightarrow r = + \widehat i + 3\widehat j + 5\widehat k$ (note that $\overrightarrow r .\overrightarrow p = 0$ ) is parallel to :
A.
$\left( { + \widehat i + 3\widehat j - 2\widehat k} \right)$
B.
$\left( { + \widehat i - 3\widehat j - 2\widehat k} \right)$
C.
$\left( { - \widehat i + 3\widehat j - 2\widehat k} \right)$
D.
$\left( { - \widehat i - 3\widehat j + 2\widehat k} \right)$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 8th January Evening Slot
Consider two charged metallic spheres S1 and
S2 of radii R1 and R2, respectively. The electric
fields E1 (on S1) and E2 (on S2) on their surfaces
are such that E1/E2 = R1/R2. Then the ratio
V1 (on S1) / V2 (on S2) of the electrostatic
potentials on each sphere is :
A.
(R1/R2)2
B.
(R2/R1)
C.
(R1/R2)3
D.
R1/R2
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 8th January Evening Slot
A particle of mass m and charge q is released
from rest in a uniform electric field. If there is
no other force on the particle, the dependence
of its speed v on the distance x travelled by it
is correctly given by (graphs are schematic and
not drawn to scale)
A.
B.
C.
D.
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 8th January Morning Slot
In finding the electric field using Gauss Law
the formula $\left| {\overrightarrow E } \right| = {{{q_{enc}}} \over {{\varepsilon _0}\left| A \right|}}$ is applicable. In the
formula ${{\varepsilon _0}}$ is permittivity of free space, A is the
area of Gaussian surface and qenc is charge
enclosed by the Gaussian surface. The equation
can be used in which of the following situation?
A.
Only when $\left| {\overrightarrow E } \right|$ = constant on the surface.
B.
For any choice of Gaussian surface.
C.
Only when the Gaussian surface is an
equipotential surface.
D.
Only when the Gaussian surface is an
equipotential surface and $\left| {\overrightarrow E } \right|$ is constant on
the surface.
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 8th January Morning Slot
Three charged particle A, B and C with charges
–4q, 2q and –2q are present on the
circumference of a circle of radius d. the charged
particles A, C and centre O of the circle formed
an equilateral triangle as shown in figure. Electric
field at O along x-direction is :
A.
${3{\sqrt 3 q} \over 4{\pi {\varepsilon _0}{d^2}}}$
B.
${{\sqrt 3 q} \over 4{\pi {\varepsilon _0}{d^2}}}$
C.
${{\sqrt 3 q} \over {\pi {\varepsilon _0}{d^2}}}$
D.
${{2\sqrt 3 q} \over {\pi {\varepsilon _0}{d^2}}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 7th January Morning Slot
Two infinite planes each with uniform surface charge density to are kept in such a way that the angle between them is 30o. The electric field in the region shown between them is given by :
A.
${\sigma \over {{ \in _0}}}\left[ {\left( {1 + {{\sqrt 3 } \over 2}} \right)\widehat y + {{\widehat x} \over 2}} \right]$
B.
${\sigma \over {2{ \in _0}}}\left[ {\left( {1 + \sqrt 3 } \right)\widehat y + {{\widehat x} \over 2}} \right]$
C.
${\sigma \over {2{ \in _0}}}\left[ {\left( {1 + \sqrt 3 } \right)\widehat y - {{\widehat x} \over 2}} \right]$
D.
${\sigma \over {2{ \in _0}}}\left[ {\left( {1 - {{\sqrt 3 } \over 2}} \right)\widehat y - {{\widehat x} \over 2}} \right]$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Evening Slot
Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $\rho $(r) = kr, where
r is the distance from the centre. Two charges A and B, of –Q each, are placed on diametrically opposite
points, at equal distance, $a$ from the centre. If A and B do not experience any force, then :
A.
$a = {8^{ - 1/4}}R$
B.
$a = {2^{ - 1/4}}R$
C.
$a = {{3R} \over {{2^{1/4}}}}$
D.
$a = {R \over {\sqrt 3 }}$
Charge enclosed in the sphere,
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Morning Slot
A point dipole $\overrightarrow p = - {p_0}\widehat x$
is kept at the origin. The potential and electric field due to this dipole on the
y-axis at a distance d are, respectively: (Take V= 0 at infinity)
A.
${{\left| {\overrightarrow p } \right|} \over {4\pi { \in _0}{d^2}}},{{ - \overrightarrow p } \over {4\pi { \in _0}{d^3}}}$
B.
$0,{{\overrightarrow p } \over {4\pi { \in _0}{d^3}}}$
C.
${{\left| {\overrightarrow p } \right|} \over {4\pi { \in _0}{d^2}}},{{\overrightarrow p } \over {4\pi { \in _0}{d^3}}}$
D.
$0,{{ - \overrightarrow p } \over {4\pi { \in _0}{d^3}}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Morning Slot
Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge
Q. At its centre is a dipole $\overrightarrow P $
as shown. In this case :
A.
surface charge density on the inner surface is uniform and equal to ${{\left( {Q/2} \right)} \over {4\pi {a^2}}}$
B.
surface charge density on the inner surface of the shell is zero everywhere
C.
surface charge density on the outer surface depends on $\left| {\overrightarrow P } \right|$
D.
electric field outside the shell is the same as that of a point charge at the centre of the shell
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Evening Slot
In free space, a particle A of charge 1$\mu $C is held fixed at a point P. Another particle B of the same charge and
mass 4$\mu $g is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P
is :
$\left[ {Take\,{1 \over {4\pi { \in _0}}} = 9 \times {{10}^9}N{m^2}{C^{ - 2}}} \right]$
A.
1.0 m/s
B.
6.32 $ \times $ 104 m/s
C.
2.0 $ \times $ 103 m/s
D.
1.5 $ \times $ 102 m/s