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Electrostatics

159 Questions Start Allen Test
All Exams Allen
Q101 Allen PYQ MCQ
In a region, the potential is represented by $V(x, y, z) = 6x - 8xy - 8y + 6yz$ , where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulombs situated at the point (1, 1, 1) is:
A.
$6\sqrt{5}$ N
B.
30 N
C.
24 N
D.
$4\sqrt{35}$ N
Q102 Allen PYQ MCQ
The electric field in a certain region is acting radially outward and is given by E = Ar. The charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by:
A.
A $\varepsilon_{0}$ a $^{2}$
B.
4 $\pi\varepsilon_{0}$ Aa $^{3}$
C.
$\varepsilon_{0}$ Aa $^{3}$
D.
4 $\pi\varepsilon_{0}$ Aa $^{2}$
Q103 Allen PYQ MCQ
If potential (in volts) in a region is expressed as V (x,y,z) = 6xy - y + 2yz, the electric field (in N/C) at point (1,1,0) is:
A.
$-(6\hat{i}+9\hat{j}+k)$
B.
$-(3\hat{i}+5\hat{j}+3k)$
C.
$-(6\hat{i}+5\hat{j}+2k)$
D.
$-(2\hat{i}+3\hat{j}+k)$
Q104 Allen PYQ MCQ
An electric dipole is placed at an angle of $30^{\circ}$ with an electric field intensity $2 \times 10^{5}$ N/C. It experiences a torque equal to 4 Nm. The charge on the dipole, if the dipole length is 2 cm, is :-
A.
5 mC
B.
7 $\mu$ C
C.
8 mC
D.
2 mC
Q105 Allen PYQ MCQ
The diagrams below show regions of equipotentials :- image.png A positive charge is moved from A to B in each diagram.
A.
In all the four cases the work done is the same
B.
Minimum work is required to move q in figure (a)
C.
Maximum work is required to move q in figure (b)
D.
Maximum work is required to move q in figure (c)
Q106 Allen PYQ MCQ
Suppose the charge of a proton and an electron differ slightly. One of them is - e, the other is (e + Δe). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given mass of hydrogen $m_{h} = 1.67 \times 10^{-27}$ kg]
A.
$10^{-23}$ C
B.
$10^{-37}$ C
C.
$10^{-47}$ C
D.
$10^{-20}$ C
Q107 Allen PYQ MCQ
An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electrical field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is :-
A.
smaller
B.
5 times greater
C.
10 times greater
D.
equal
Q108 Allen PYQ MCQ
A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre:
A.
increases as r increases for r < R and for r > R
B.
zero as r increases for r < R, decreases as r increases for r > R
C.
zero as r increases for r < R, increases as r increases for r > R
D.
decreases as r increases for r < R and for r > R
Q109 Allen PYQ MCQ
Two parallel infinite line charges with linear charge densities +λ C/m and -λ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?
A.
zero
B.
$\frac{2\lambda}{\pi\in_{0}R}N/C$
C.
$\frac{\lambda}{\pi\in_{0}R}N/C$
D.
$\frac{\lambda}{2\pi\in_{0}R}N/C$
Q110 Allen PYQ MCQ
Two point charges A and B, having charges +Q and -Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes:
A.
F
B.
$\frac{9F}{16}$
C.
$\frac{16F}{9}$
D.
$\frac{4F}{3}$
Q111 Allen PYQ MCQ
A sphere encloses an electric dipole with charge $\pm3\times10^{-6}$ C. What is the total electric flux across the sphere?
A.
$-3\times10^{-6}$ Nm $^{2}$ /C
B.
zero
C.
$3\times10^{-6}$ Nm $^{2}$ /C
D.
$6\times10^{-6}$ Nm $^{2}$ /C
Q112 Allen PYQ MCQ
A short electric dipole has a dipole moment of $16 \times 10^{-9}$ C m. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of $60^{\circ}$ with the dipole axis is: $\left(\frac{1}{4\pi\epsilon_{0}}=9\times10^{9}\mathrm{Nm}^{2}/\mathrm{C}^{2}\right)$
A.
zero
B.
50 V
C.
200 V
D.
400 V
Q113 Allen PYQ MCQ
In a certain region of space with volume $0.2 \, m^{3}$ the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is:
A.
5 N/C
B.
Zero
C.
0.5 N/C
D.
1 N/C
Q114 Allen PYQ MCQ
A spherical conductor of radius 10 cm has a charge of $3.2 \times 10^{-7}$ C distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere? ( $\frac{1}{4\pi \in_{0}} = 9 \times 10^{9} \, Nm^{2}/C^{2}$ )
A.
$1.28 \times 10^{7} \, N/C$
B.
$1.28 \times 10^{4} \, N/C$
C.
$1.28 \times 10^{5} \, N/C$
D.
$1.28 \times 10^{6} \, N/C$
Q115 Allen PYQ MCQ
The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having dipole moment $\vec{p}$ is given by (r >> separation of two charges forming the dipole, $\in0$ -permittivity of free space)
A.
$\vec{E} = \frac{\vec{p}}{4\pi \in_{0} r^{3}}$
B.
$\vec{E} = \frac{2\vec{p}}{4\pi \in_{0} r^{3}}$
C.
$\vec{E} = -\frac{\vec{p}}{4\pi \in_{0} r^{2}}$
D.
$\vec{E} = -\frac{\vec{p}}{4\pi \in_{0} r^{3}}$
Q116 Allen PYQ MCQ
The acceleration of an electron due to the mutual attraction between the electron and a proton when they are $1.6 \, Å$ apart is, $(m_{e} \simeq 9 \times 10^{-31} \, kg, e = 1.6 \times 10^{-19} \, C)$ (Take $\frac{1}{4\pi\varepsilon_{0}} = 9 \times 10^{9} \, Nm^{2} \, C^{-2}$ )
A.
$10^{24} \, m/s^{2}$
B.
$10^{23} \, m/s^{2}$
C.
$10^{22} \, m/s^{2}$
D.
$10^{25} \, m/s^{2}$
Q117 Allen PYQ MCQ
The variation of electrostatic potential with radial distance $r$ from the centre of a positively charged metallic thin shell of radius $R$ is given by the graph
A.
B.
C.
D.
Q118 Allen PYQ MCQ
A dipole is placed in an electric field as shown. In which direction will it move?
A.
towards the left as its potential energy will increase.
B.
towards the right as its potential energy will decrease.
C.
towards the left as its potential energy will decrease.
D.
towards the right as its potential energy will increase.
Q119 Allen PYQ MCQ
Two charged spherical conductors of radius $R_{1}$ and $R_{2}$ are connected by a wire. Then the ratio of surface charge densities of the spheres ( $\sigma_{1}/\sigma_{2}$ ) is:
A.
$\frac{R_{1}}{R_{2}}$
B.
$\frac{R_{2}}{R_{1}}$
C.
$\sqrt{\left(\frac{R_{1}}{R_{2}}\right)}$
D.
$\frac{R_{1}^{2}}{R_{2}^{2}}$
Q120 Allen PYQ MCQ
The angle between the electric lines of force and the equipotential surface is :
A.
$45^{\circ}$
B.
$90^{\circ}$
C.
$180^{\circ}$
D.
$0^{\circ}$
Q121 Allen PYQ MCQ
Two point charges -q and +q are placed at a distance of L, as shown in the figure. The magnitude of electric field intensity at a distance R (R >> L) varies as :
A.
$\frac{1}{R^{3}}$
B.
$\frac{1}{R^{4}}$
C.
$\frac{1}{R^{6}}$
D.
$\frac{1}{R^{2}}$
Q122 Allen PYQ MCQ
Six charges +q, -q, +q, -q, +q and -q are fixed at the corners of a hexagon of side d as shown in the figure. The work done in bringing a charge $q_{0}$ to the centre of the hexagon from infinity is: ( $\varepsilon_{0}$ - permittivity of free space)
A.
Zero
B.
$\frac{-\mathbf{q}^2}{4\pi\varepsilon_0\mathbf{d}}$
C.
$\frac{-\mathrm{q}^2}{4\pi\varepsilon_0\mathrm{d}}\left(3 - \frac{1}{\sqrt{2}}\right)$
D.
$\frac{-\mathbf{q}^2}{4\pi\varepsilon_0\mathbf{d}}\left(6 - \frac{1}{\sqrt{2}}\right)$
Q123 Allen PYQ MCQ
An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $2 \times 10^{5}$ NC $^{-1}$ . It experiences a torque equal to 4 Nm. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm.
A.
6 mC
B.
4 mC
C.
2 mC
D.
8 mC
Q124 Allen PYQ MCQ
If $\oint_{S} \vec{E} \cdot d\vec{S} = 0$ over a surface, then:
A.
the magnitude of electric field on the surface is constant.
B.
all the charges must necessarily be inside the surface.
C.
the electric field inside the surface is necessarily uniform.
D.
the number of flux lines entering the surface must be equal to the number of flux lines leaving it.
Q125 Allen PYQ MCQ
An electric dipole is placed as shown in the figure. The electric potential (in $10^{2}$ V) at point P due to the dipole is ( $\epsilon_{0}=$ permittivity of free space and $\frac{1}{4\pi\epsilon_{0}}=K$ ):
A.
$\left(\frac{5}{8}\right)qK$
B.
$\left(\frac{8}{5}\right)qK$
C.
$\left(\frac{8}{3}\right)qK$
D.
$\left(\frac{3}{8}\right)qK$