2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Morning Slot
A uniformly charged ring of radius 3a and total
charge q is placed in xy-plane centred at origin.
A point charge q is moving towards the ring
along the z-axis and has speed u at z = 4a. The
minimum value of u such that it crosses the
origin is :
A.
$\sqrt {{2 \over m}} {\left( {{2 \over {15}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}$
B.
$\sqrt {{2 \over m}} {\left( {{1 \over {15}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}$
C.
$\sqrt {{2 \over m}} {\left( {{1 \over {5}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}$
D.
$\sqrt {{2 \over m}} {\left( {{4 \over {15}}{{{q^2}} \over {4\pi {\varepsilon _0}a}}} \right)^{1/2}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Evening Slot
Four point charges –q, +q, +q and –q are placed
on y-axis at y = –2d, y = –d, y = +d and
y = +2d, respectively. The magnitude of the
electric field E at a point on the x-axis at
x = D, with D >> d, will behave as :-
A.
$E \propto {1 \over D^3}$
B.
$E \propto {1 \over D}$
C.
$E \propto {1 \over D^4}$
D.
$E \propto {1 \over D^2}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Morning Slot
A system of three charges are placed as shown
in the figure :
If D >> d, the potential energy of the system is
best given by :
If D >> d, the potential energy of the system is
best given by :
A.
${1 \over {4\pi {\varepsilon _0}}}\left[ { {{{q^2}} \over d} + {{qQd} \over {{D^2}}}} \right]$
B.
${1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} - {{qQd} \over {2{D^2}}}} \right]$
C.
${1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} - {{qQd} \over {{D^2}}}} \right]$
D.
${1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} + {2{qQd} \over {{D^2}}}} \right]$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Evening Slot
A positive point charge is released from rest at
a distance r0 from a positive line charge with
uniform density. The speed (v) of the point
charge, as a function of instantaneous distance
r from line charge, is proportional to :-
A.
$v \propto \left( {{r \over {{r_0}}}} \right)$
B.
$v \propto \ln \left( {{r \over {{r_0}}}} \right)$
C.
$v \propto {e^{ + r/{r_0}}}$
D.
$v \propto \sqrt {\ln \left( {{r \over {{r_0}}}} \right)} $
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Evening Slot
The electric field in a region is given by
$\mathop E\limits^ \to = \left( {Ax + B} \right)\mathop i\limits^ \wedge $
, where E is in NC–1 and x is in
metres. The values of constants are
A = 20 SI unit and B = 10 SI unit. If the potential
at x = 1 is V1 and that at x = –5 is V2, then
V1 – V2 is :-
A.
–520 V
B.
180 V
C.
–48 V
D.
320 V
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Morning Slot
The bob of a simple pendulum has mass 2g and
a charge of 5.0 μC. It is at rest in a uniform
horizontal electric field of intensity 2000 V/m.
At equilibrium, the angle that the pendulum
makes with the vertical is : (take g = 10 m/s2)
A.
tan–1(5.0)
B.
tan–1(2.0)
C.
tan–1(0.5)
D.
tan–1(0.2)
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Morning Slot
A solid conducting sphere, having a charge Q,
is surrounded by an uncharged conducting
hollow spherical shell. Let the potential
difference between the surface of the solid
sphere and that of the outer surface of the
hollow shell be V. If the shell is now given a
charge of –4 Q, the new potential difference
between the same two surfaces is :
A.
V
B.
2V
C.
–2V
D.
4V
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Morning Slot
Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure :
A.
$2q\ell \widehat j$
B.
$\left( {q\ell } \right){{\widehat i + \widehat j} \over {\sqrt 2 }}$
C.
$\sqrt 3 \,q\ell {{\widehat j - \widehat i} \over {\sqrt 2 }}$
D.
$ - \sqrt 3 \,q\ell \widehat j$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Morning Slot
There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V (R(t)) of the distribution as a function of its instantaneous radius R (t) is :
A.
B.
C.
D.
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Evening Slot
An electric field of 1000 V/m is applied to an electric dipole at angle of 45o. The value of electric dipole moment is 10–29 C.m. What is the potential energy of the electric dipole?
A.
- 7 $ \times $ 10–27 J
B.
$-$ 9 $ \times $ 10–20 J
C.
$-$ 10 $ \times $ 10–29 J
D.
$-$ 20 $ \times $ 10–18 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Morning Slot
Three charges Q, + q and + q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is :
A.
${{ - q} \over {1 + \sqrt 2 }}$
B.
+ q
C.
$-$ 2q
D.
${{ - \sqrt 2 q} \over {\sqrt 2 + 1}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Morning Slot
The given graph shows variation (with distance r form centre) of :
A.
Electric field of a uniformly charged sphere
B.
Electric field of a uniformly charged spherical shell
C.
Potential of a uniformly charged sphere
D.
Potential of a uniformly charged spherical shell
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Evening Slot
Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and (0, –2). The work required to put a fifth charge Q at the origin of the coordinate system will be -
A.
${{{Q_2}} \over {4\pi {\varepsilon _0}}}$
B.
${{{Q^2}} \over {2\sqrt 2 \pi {\varepsilon _0}}}$
C.
${{{Q_2}} \over {4\pi {\varepsilon _0}}}\left( {1 + {1 \over {\sqrt 3 }}} \right)$
D.
${{{Q_2}} \over {4\pi {\varepsilon _0}}}\left( {1 + {1 \over {\sqrt 5 }}} \right)$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Evening Slot
Charges –q and +q located at A and B, respectively, constitude an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P' such that OP' = $\left( {{y \over 3}} \right)$, the force on Q will be close to - $\left( {{y \over 3} > > 2a} \right)$
A.
9F
B.
3F
C.
F/3
D.
27F
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Morning Slot
A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be -
A.
${{Q\left( {{a^2} + {b^2} + {c^2}} \right)} \over {4\pi {\varepsilon _0}\left( {{a^3} + {b^3} + {c^3}} \right)}}$
B.
${Q \over {4\pi {\varepsilon _0}\left( {a + b + c} \right)}}$
C.
${Q \over {12\pi {\varepsilon _0}}}{{ab + bc + ca} \over {abc}}$
D.
${{Q\left( {a + b + c} \right)} \over {4\pi {\varepsilon _0}\left( {{a^2} + {b^2} + {c^2}} \right)}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Morning Slot
Two electric dipoles, A, B with respective dipole moments ${\overrightarrow d _A} = - 4qai$ and ${\overrightarrow d _B} = - 2qai$ are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -
A.
${{\sqrt 2 R} \over {\sqrt 2 + 1}}$
B.
${R \over {\sqrt 2 + 1}}$
C.
${{\sqrt 2 R} \over {\sqrt 2 - 1}}$
D.
${R \over {\sqrt 2 - 1}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Evening Slot
Two point charges q1$\left( {\sqrt {10} \mu C} \right)$ and q2($-$ 25 $\mu $C) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is,
[take ${1 \over {4\pi { \in _0}}}$ = 9 $ \times $ 109 Nm2C$-$2]
[take ${1 \over {4\pi { \in _0}}}$ = 9 $ \times $ 109 Nm2C$-$2]
A.
$\left( {63\widehat i - 27\widehat j} \right) \times {10^2}$
B.
$\left( { - 63\widehat i + 27\widehat j} \right) \times {10^2}$
C.
$\left( {81\widehat i - 81\widehat j} \right) \times {10^2}$
D.
$\left( { - 81\widehat i + 81\widehat j} \right) \times {10^2}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Evening Slot
Charge is distributed within a sphere of radius R with a volume charge density $\rho \left( r \right) = {A \over {{r^2}}}{e^{ - {{2r} \over s}}},$ where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :
A.
a log $\left( {1 - {Q \over {2\pi aA}}} \right)$
B.
${a \over 2}$ log $\left( {{1 \over {1 - {Q \over {2\pi aA}}}}} \right)$
C.
a log $\left( {{1 \over {1 - {Q \over {2\pi aA}}}}} \right)$
D.
${a \over 2}$ log $\left( {1 - {Q \over {2\pi aA}}} \right)$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Morning Slot
Three charges + Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, placed at x = 0, is zero, then value of q is :
A.
$-$ ${Q \over 4}$
B.
+ ${Q \over 2}$
C.
+ ${Q \over 4}$
D.
$-$ ${Q \over 2}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Morning Slot
For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is :
A.
${R \over {\sqrt 5 }}$
B.
${R \over {\sqrt 2 }}$
C.
R
D.
R$\sqrt 2 $
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 16th April Morning Slot
Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between theis F. A third identical conducting sphere, C, is uncharged. Sphere C is first touhed to A, then to B, and then removed. As a result, the force between A and B would be equal to :
A.
F
B.
${{3F} \over 4}$
C.
${{3F} \over 8}$
D.
${{F} \over 2}$
2018
JEE Mains
MCQ
JEE Main 2018 (Offline)
Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge
densities $ + \sigma $, $ - \sigma $ and $ + \sigma $ respectively. The potential of shell B is :
A.
${\sigma \over { \in {}_0}}\left[ {{{{b^2} - {c^2}} \over c} + a} \right]$
B.
${\sigma \over { \in {}_0}}\left[ {{{{a^2} - {b^2}} \over a} + c} \right]$
C.
${\sigma \over { \in {}_0}}\left[ {{{{a^2} - {b^2}} \over b} + c} \right]$
D.
${\sigma \over { \in {}_0}}\left[ {{{{b^2} - {c^2}} \over b} + a} \right]$
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 15th April Evening Slot
A solid ball of radius R has a charge density $\rho $
given by $\rho $ = $\rho $o (1 $-$ ${\raise0.5ex\hbox{$\scriptstyle r$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle R$}}$) for 0 $ \le $ r $ \le $ R. The electric field outside the ball is :
given by $\rho $ = $\rho $o (1 $-$ ${\raise0.5ex\hbox{$\scriptstyle r$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle R$}}$) for 0 $ \le $ r $ \le $ R. The electric field outside the ball is :
A.
${{{\rho _o}{R^3}} \over {{ \in _o}{r^2}}}$
B.
${{{\rho _o}{R^3}} \over {12{ \in _o}{r^2}}}$
C.
${{4{\rho _o}{R^3}} \over {3{ \in _o}{r^2}}}$
D.
${{3{\rho _o}{R^3}} \over {4{ \in _o}{r^2}}}$
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 15th April Morning Slot
A body of mass $M$ and charge $q$ is connected to spring of spring constant $k.$ It is oscillating along $x$-direction about its equilibrium position, taken to be at $x=0,$ with an amplitude $A$. An electric field $E$ is applied along the $x$-direction. Which of the following statements is correct ?
A.
The new equilibrium position is at a distance ${{qE} \over {2k}}$ from $x=0.$
B.
The total energy of the system is ${1 \over 2}m{\omega ^2}{A^2} + {1 \over 2}{{{q^2}{E^2}} \over k}.$
C.
The total energy of the system is ${1 \over 2}m{\omega ^2}{A^2} - {1 \over 2}{{{q^2}{E^2}} \over k}.$
D.
The new equilibrium position is at a distance ${{2qE} \over k}$ from $x=0.$
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 15th April Morning Slot
A charge $Q$ is placed at a distance $a/2$ above the center of the square surface of edge a as shown in the figure.
The electric flux through the square surface is
The electric flux through the square surface is
A.
${Q \over {{ \in _0}}}$
B.
${Q \over {2{ \in _0}}}$
C.
${Q \over {3{ \in _0}}}$
D.
${Q \over {6{ \in _0}}}$
2017
JEE Mains
MCQ
JEE Main 2017 (Online) 9th April Morning Slot
Four closed surfaces and corresponding charge distributions are shown below.
Let the respective electric fluxes through the surfaces be ${\Phi _1},$ ${\Phi _2},$ ${\Phi _3}$ and ${\Phi _4}$. Then :
Let the respective electric fluxes through the surfaces be ${\Phi _1},$ ${\Phi _2},$ ${\Phi _3}$ and ${\Phi _4}$. Then :
A.
${\Phi _1}$ < ${\Phi _2}$ = ${\Phi _3}$ > ${\Phi _4}$
B.
${\Phi _1}$ > ${\Phi _2}$ > ${\Phi _3}$ > ${\Phi _4}$
C.
${\Phi _1}$ = ${\Phi _2}$ = ${\Phi _3}$ = ${\Phi _4}$
D.
${\Phi _1}$ > ${\Phi _3}$ ; ${\Phi _2}$ < ${\Phi _4}$
2017
JEE Mains
MCQ
JEE Main 2017 (Online) 8th April Morning Slot
There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $P,$ in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60o with the direction of the field ?
A.
589.5 V
B.
589.2 V
C.
589.4 V
D.
589.6 V
2017
JEE Mains
MCQ
JEE Main 2017 (Offline)
An electric dipole has a fixed dipole moment $\overrightarrow p $, which makes angle $\theta$ with respect to x-axis. When
subjected to an electric field $\mathop {{E_1}}\limits^ \to = E\widehat i$ , it experiences a torque $\overrightarrow {{T_1}} = \tau \widehat k$ . When subjected to another electric
field $\mathop {{E_2}}\limits^ \to = \sqrt 3 {E_1}\widehat j$ it experiences a torque $\mathop {{T_2}}\limits^ \to = \mathop { - {T_1}}\limits^ \to $ . The angle $\theta$ is:
A.
90o
B.
45o
C.
30o
D.
60o
2016
JEE Mains
MCQ
JEE Main 2016 (Online) 10th April Morning Slot
Within a spherical charge distribution of charge density $\rho $(r), N equipotential surfaces of potential V0, V0 + $\Delta $V, V0 + 2$\Delta $V, .......... V0 + N$\Delta $V ($\Delta $ V > 0), are drawn and have increasing radii r0, r1, r2,..........rN, respectively. If the difference in the radii of the surfaces is constant for all values of V0 and $\Delta $V then :
A.
$\rho $ (r) $\alpha $ r
B.
$\rho $ (r) = constant
C.
$\rho $ (r) $\alpha $ ${1 \over r}$
D.
$\rho $ (r) $\alpha $ ${1 \over {{r^2}}}$
2016
JEE Mains
MCQ
JEE Main 2016 (Online) 9th April Morning Slot
The potential (in volts) of a charge distribution is given by.
V(z) = 30 $-$ 5x2 for $\left| z \right|$ $ \le $ 1 m.
V(z) = 35 $-$ 10 $\left| z \right|$ for $\left| z \right|$ $ \ge $1 m.
V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume ${\rho _0}$ (in units of ${\varepsilon _0}$) which is spread over a certain region, then choose the correct statement.
V(z) = 30 $-$ 5x2 for $\left| z \right|$ $ \le $ 1 m.
V(z) = 35 $-$ 10 $\left| z \right|$ for $\left| z \right|$ $ \ge $1 m.
V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume ${\rho _0}$ (in units of ${\varepsilon _0}$) which is spread over a certain region, then choose the correct statement.
A.
${\rho _0}$ = 10 ${\varepsilon _0}$ for $\left| z \right|$ $ \le $ 1 m and ${\rho _0} = 0$ elsewhere
B.
${\rho _0}$ = 20 ${\varepsilon _0}$ in the entire region
C.
${\rho _0}$ = 40 ${\varepsilon _0}$ in the entire region
D.
${\rho _0}$ = 20 ${\varepsilon _0}$ for $\left| z \right|$ $ \le $ 1 m and ${\rho _0} = 0$ elsewhere
2016
JEE Mains
MCQ
JEE Main 2016 (Offline)
The region between two concentric spheres of radii $'a'$ and $'b',$ respectively (see figure), have volume charge density $\rho = {A \over r},$ where $A$ is a constant and $r$ is the distance from the center. A such that the electric field in the region between the spheres will be constant, is :
A.
${{2Q} \over {\pi \left( {{a^2} - {b^2}} \right)}}$
B.
${{2Q} \over {\pi \,{a^2}}}$
C.
${Q \over {2\pi \,{a^2}}}$
D.
${Q \over {2\pi \,\left( {{b^2} - {a^2}} \right)}}$
2015
JEE Mains
MCQ
JEE Main 2015 (Offline)
A long cylindrical shell carries positives surfaces change $\sigma $ in the upper half and negative surface charge - $\sigma $ in the lower half. The electric field lines around the cylinder will look like figure given in :
(figures are schematic and not drawn to scale)
(figures are schematic and not drawn to scale)
A.
B.
C.
D.
2014
JEE Mains
MCQ
JEE Main 2014 (Offline)
Assume that an electric field $\overrightarrow E = 30{x^2}\widehat i$ exists in space. Then the potential difference ${V_A} - {V_O},$ where ${V_O}$ is the potential at the origin and ${V_A}$ the potential at $x=2$ $m$ is :
A.
$120$ $J/C$
B.
$-120$ $J/C$
C.
$-80$ $J/C$
D.
$80$ $J/C$
2013
JEE Mains
MCQ
JEE Main 2013 (Offline)
Two charges, each equals to $q,$ are kept at $x=-a$ and $x=a$ on the $x$-axis. A particle of mass $m$ and charge ${q_0} = {q \over 2}$ is placed at the origin. If charge ${q_0}$ is given a small displacement $\left( {y < < a} \right)$ along the $y$-axis, the net force acting on the particle is proportional to
A.
$y$
B.
$-y$
C.
${1 \over y}$
D.
$-{1 \over y}$
2013
JEE Mains
MCQ
JEE Main 2013 (Offline)
A charge $Q$ is uniformly distributed over a long rod $AB$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at distance $L$ from the end $A$ is
A.
${Q \over {8\pi {\varepsilon _0}L}}$
B.
${{3Q} \over {4\pi {\varepsilon _0}L}}$
C.
${Q \over {4\pi {\varepsilon _0}L\,\ln \,2}}$
D.
${{Q\ln \,2} \over {4\pi {\varepsilon _0}L\,{}^s}}$
2012
JEE Mains
MCQ
AIEEE 2012
This question has statement- $1$ and statement- $2.$ Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho $. As a result of this uniform charge distribution there is a finite value of electric potential at the center of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.
An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho $. As a result of this uniform charge distribution there is a finite value of electric potential at the center of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.
Statement- $1:$ When a charge $q$ is take from the centre of the surface of the sphere its potential energy changes by ${{q\rho } \over {3{\varepsilon _0}}}$
Statement- $2:$ The electric field at a distance $r\left( {r < R} \right)$ from the center of the sphere is ${{\rho r} \over {3{\varepsilon _0}}}.$
A.
Statement- $1$ is true, Statement- $2$ is true; Statement- $2$ is not the correct explanation of Statement- $1$.
B.
Statement $1$ is true, Statement $2$ is false.
C.
Statement $1$ is false, Statement $2$ is true.
D.
Statement- $1$ is true, Statement- $2$ is true; Statement- $2$ is the correct explanation of Statement- $1$.
2012
JEE Mains
MCQ
AIEEE 2012
In a uniformly charged sphere of total charge $Q$ and radius $R,$ the electric field $E$ is plotted as function of distance from the center. The graph which would correspond to the above will be:
A.
B.
C.
D.
2011
JEE Mains
MCQ
AIEEE 2011
Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d\left( {d < < 1} \right)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity $v$. Then as a function of distance $x$ between them,
A.
$v\, \propto \,{x^{ - 1}}$
B.
$y\, \propto \,{x^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}$
C.
$v\, \propto \,x$
D.
$v\, \propto \,{x^{ - {\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}$
2011
JEE Mains
MCQ
AIEEE 2011
The electrostatic potential inside a charged spherical ball is given by $\phi = a{r^2} + b$ where $r$ is the distance from the center and $a,b$ are constants. Then the charge density inside the ball is:
A.
$ - 6a{\varepsilon _0}r$
B.
$ - 24\pi a{\varepsilon _0}$
C.
$ - 6a{\varepsilon _0}$
D.
$ - 24\pi {\varepsilon _0}r$
2010
JEE Mains
MCQ
AIEEE 2010
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of ${30^ \circ }$ with each other. When suspended in a liquid of density $0.8g$ $c{m^{ - 3}},$ the angle remains the same. If density of the material of the sphere is $1.6$ $g$ $c{m^{ - 3}},$ the dielectric constant of the liquid is
A.
$4$
B.
$3$
C.
$2$
D.
$1$
2010
JEE Mains
MCQ
AIEEE 2010
A thin semi-circular ring of radius $r$ has a positive charges $q$ distributed uniformly over it. The net field $\overrightarrow E $ at the center $O$ is
A.
${q \over {4{\pi ^2}{\varepsilon _0}{r^2}}}\,j$
B.
$ - {q \over {4{\pi ^2}{\varepsilon _0}{r^2}}}\,j$
C.
$ - {q \over {2{\pi ^2}{\varepsilon _0}{r^2}}}\,j$
D.
$ {q \over {2{\pi ^2}{\varepsilon _0}{r^2}}}\,j$
2010
JEE Mains
MCQ
AIEEE 2010
Let there be a spherically symmetric charge distribution with charge density varying as $\rho \left( r \right) = {\rho _0}\left( {{5 \over 4} - {r \over R}} \right)$ upto $r=R,$ and $\rho \left( r \right) = 0$ for $r>R,$ where $r$ is the distance from the erigin. The electric field at a distance $r\left( {r < R} \right)$ from the origin is given by
A.
${{{\rho _0}r} \over {4{\varepsilon _0}}}\left( {{5 \over 3} - {r \over R}} \right)$
B.
${{4\pi {\rho _0}r} \over {3{\varepsilon _0}}}\left( {{5 \over 3} - {r \over R}} \right)$
C.
${{4{\rho _0}r} \over {4{\varepsilon _0}}}\left( {{5 \over 4} - {r \over R}} \right)$
D.
${{{\rho _0}r} \over {3{\varepsilon _0}}}\left( {{5 \over 4} - {r \over R}} \right)$
2009
JEE Mains
MCQ
AIEEE 2009
Let $P\left( r \right) = {Q \over {\pi {R^4}}}r$ be the change density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $'p'$ inside the sphere at distance ${r_1}$ from the center of the sphere, the magnitude of electric field is :
A.
${Q \over {4\pi \,{ \in _0}\,r_1^2}}$
B.
${{Qr_1^2} \over {4\pi \,{ \in _0}\,{R^4}}}$
C.
${{Qr_1^2} \over {3\pi \,{ \in _0}\,{R^4}}}$
D.
$0$
2009
JEE Mains
MCQ
AIEEE 2009
A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $Q/q$ equals:
A.
$-1$
B.
$1$
C.
$ - {1 \over {\sqrt 2 }}$
D.
$ - 2\sqrt 2 $
2009
JEE Mains
MCQ
AIEEE 2009
Two points $P$ and $Q$ are maintained at the potentials of $10$ $V$ and $-4$ $V$, respectively. The work done in moving $100$ electrons from $P$ to $Q$ is :
A.
$9.60 \times {10^{ - 17}}J$
B.
$ - 2.24 \times {10^{ - 16}}J$
C.
$ 2.24 \times {10^{ - 16}}J$
D.
$- 9.60 \times {10^{ - 17}}J$
2009
JEE Mains
MCQ
AIEEE 2009
(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.)
Statement-1 : For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q.$
Statement-2 : The net work done by a conservative force on an object moving along a closed loop is zero.
A.
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
B.
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
C.
Statement- 1 is false, Statement- 2 is true.
D.
Statement- 1 true, Statement- 2 is false
2008
JEE Mains
MCQ
AIEEE 2008
A thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E(r)$ produced by the shell in the range $0 \le r < \infty ,$ where $r$ is the distance from the center of the shell?
A.
B.
c
c
C.
D.
2007
JEE Mains
MCQ
AIEEE 2007
Charges are placed on the vertices of a square as shown. Let $\overrightarrow E $ be the electric field and $V$ the potential at the center. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively, then
A.
$\overrightarrow E $ changes, $V$ remains unchanged
B.
$\overrightarrow E $ remains unchanged, $V$ changes
C.
both $\overrightarrow E $ and $V$ change
D.
$\overrightarrow E $ and $V$ remain unchanged
2007
JEE Mains
MCQ
AIEEE 2007
The potential at a point $x$ (measured in $\mu \,m$) due to some charges situated on the $x$-axis is given by $V\left( x \right) = 20/\left( {{x^2} - 4} \right)$ volt
The electric field $E$ at $x = 4\,\mu \,m$ is given by
The electric field $E$ at $x = 4\,\mu \,m$ is given by
A.
$(10/9)$ volt / $\mu $ $m$ and in the $ + ve$ $x$ direction
B.
$\left( {5/3} \right)$ volt/ $\mu $ $m$ and in the $-ve$ $x$ direction
C.
$\left( {5/3} \right)$ volt/$\mu $ $m$ and in the $+ve$ $x$ direction
D.
$\left( {10/9} \right)$ volt/ $\mu \,m$ and in the $-ve$ $x$ direction
2007
JEE Mains
MCQ
AIEEE 2007
An electric charge ${10^{ - 3}}\,\,\mu \,C$ is placed at the origin $(0,0)$ of $X-Y$ co-ordinate system. Two points $A$ and $B$ are situated at $\left( {\sqrt 2 ,\sqrt 2 } \right)$ and $\left( {2,0} \right)$ respectively. The potential difference between the points $A$ and $B$ will be
A.
$4.5$ volts
B.
$9$ volts
C.
zero
D.
$2$ volts
