Electric Field

Q.

Can a single charge create an electric field?

Q. A charged particle of mass $m=1\text{kg}$ and charge $q=2\mu C$ is thrown from the ground at an angle $\theta ={45}^{\circ }$ with the horizontal, with initial speed $20\text{m/s}$. In the space a horizontal electric field of magnitude $E=2\times {10}^7\text{V/m}$ exists. Find the range covered by the projectile on the horizontal ground. $[g=10{\text{m/s}}^2]$

1. $200\text{m}$
2. $150\text{m}$
3. $100\text{m}$
4. $170\text{m}$

Q. The intensity of the electric field required to keep a water drop of radius ${10}^{-5}$ cm, just suspended in air when charged with one electron is approximately (g = 10newton / kg, e$=1.6\times {10}^{-19}$ coulomb)

1. 260 volt / cm
2. 260 newton / coulomb
3. 130 volt / cm
4. 130 newton / coulomb

Q. A particle of charge $q$ and mass $m$ moves rectilinearly under the action of an electric field $E=\alpha -\beta x$. Here, $\alpha$ and $\beta$ are positive constants and $x$ is the distance from the point where the particle was initially at rest. Then,

1. The motion of the particle is oscillatory
2. The amplitude of the particle is $\left(\frac{\alpha }{\beta }\right)$
3. The mean position of the particle is at $x=\left(\frac{\alpha }{\beta }\right)$
4. The maximum acceleration of the particle is $\frac{q\alpha }{m}$

Q. A uniformly charged ring with radius $0.5\text{m}$ has $0.002\pi \text{m}$ gap. If the ring carries a charge of $+1\text{C}$, the electric field at the centre is

1. $7.5\times {10}^7{\text{NC}}^{-1}$
2. $6.2\times {10}^7{\text{NC}}^{-1}$
3. $6.5\times {10}^7{\text{NC}}^{-1}$
4. $7.2\times {10}^7{\text{NC}}^{-1}$

Q. The electric field in a region is given by $\overrightarrow{E}=(1200\hat{i}+1600\hat{j})\text{N/C}$. Find the flux of this field through a rectangular surface of area $0.2{\text{m}}^2$ parallel to the $y-z$ plane.

1. $140{\text{N-m}}^2/\text{C}$
2. $440{\text{N-m}}^2/\text{C}$
3. $340{\text{N-m}}^2/\text{C}$
4. $240{\text{N-m}}^2/\text{C}$

Q. If the shown system is in equilibrium, then the surface charge density on the large sheet is
[Take ${ϵ}_0=9\times {10}^{-12}{\text{C}}^2{\text{/Nm}}^2$ and $g=10{\text{m/s}}^2$]

1. $7.8\times {10}^{-7}{\text{C/m}}^2$
2. $4.8\times {10}^{-7}{\text{C/m}}^2$
3. $6.8\times {10}^{-7}{\text{C/m}}^2$
4. $5.8\times {10}^{-7}{\text{C/m}}^2$

Q. A particle moves from a point $\left(-2\hat{i}+5\hat{j}\right)$ to $\left(4\hat{j}+3\hat{k}\right)$ when a force of $\left(4\hat{i}+3\hat{j}\right)$$N$ is applied. How much work has been done by the force ?

1. $5J$
2. $2J$
3. $8J$
4. $11J$

Q. A charged particle is projected perpendicular to a uniform electric field of length $2\text{m}$ and initial velocity of charged particle is $10\text{m/s}$. Calculate deflection of the charge in the direction of electric field., when it leaves it.

1. $4\text{mm}$
2. $6\text{mm}$
3. $8\text{mm}$
4. $9\text{mm}$

Q. A point charge$(+10\text{nC})$ is kept at point $P(1,2,3)$ and a test charge is kept at point $Q(3,4,5)$. Find the electric field experienced by the test charge.
$[$Assume distances in metre$]$

1. $3.3(\hat{i}+\hat{j}+\hat{k})\text{N/C}$
2. $2.2(\hat{i}+\hat{j}+\hat{k})\text{N/C}$
3. $4.4(\hat{i}+\hat{j}+\hat{k})\text{N/C}$
4. $5.5(\hat{i}+\hat{j}+\hat{k})\text{N/C}$

Q.

A point charge produces an electric field of magnitude $5.0{\text{NC}}^{-1}$ at a distance of 40 cm from it. What is the magnitude of charge?

1. $8.9\text{C}$

2. $8.9\times {10}^{-11}\text{C}$

3. $-8.9\times {10}^{11}\text{C}$

4. ${10}^{-11}\text{C}$

Q. Two charges $Q$ & $-Q$ are kept at some distance, so that electric field at the mid point is $\overrightarrow{E}$. Find the force on $Q$ due to the field of $-Q$. (charges are isolated)

1. $\frac{Q\overrightarrow{E}}{4}$
2. $4Q\overrightarrow{E}$
3. $\frac{Q\overrightarrow{E}}{8}$
4. $\frac{Q\overrightarrow{E}}{2}$

Q.

Three infinite long plane sheets carrying uniform charge densities
${\sigma }_1=-\sigma ,{\sigma }_2=+2\sigma$ and ${\sigma }_3=+3\sigma$ are placed parallel to the x-z plane at y =a, y=3a and y=4a as shown in Fig. 20.18. The electric field at point P is

1. zero

2. $-\frac{2\sigma }{{ϵ}_0}\hat{j}$

3. $-\frac{3\sigma }{{ϵ}_0}\hat{j}$

4. $\frac{3\sigma }{{ϵ}_0}\hat{j}$

Q. A charged particle is projected perpendicular to a uniform electric field of length $2\text{m}$ and initial velocity of charged particle is $10\text{m/s}$. Calculate deflection of the charge in the direction of electric field., when it leaves it.

1. $4\text{mm}$
2. $6\text{mm}$
3. $8\text{mm}$
4. $9\text{mm}$

Q. An electron gun $\text{G}$ emits electrons of energy $2\text{keV}$ travelling in the positive $x$ - direction. The electrons are required to hit the spot of $\text{S}$ where $\text{GS}=0.1\text{m}$, and the line $\text{GS}$ makes an angle of ${60}^{\circ }$ with the $x$ - axis as shown in figure. If a uniform magnetic field $\overrightarrow{B}$ parallel to $\text{GS}$ exists in the region outside the electron gun , then minimum value of $B$ needed to make the electron hit $\text{S}$ is $k\text{mT}$ Find the value of k (Give the nearest integer value)

Q. The nuclear charge $\left(Ze\right)$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho \left(r\right)$( charge per unit volume) is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction. The electric field within the nucleus is generally observed to be linearly dependent on $r$. This implies

1. $a=R$
2. $a=\frac{2R}{3}$
3. $a=\frac{R}{2}$
4. $a=0$

Q. For the given arrangement of charges, charges $1$ and $2$ are fixed. A third charge at mid of line joining charges $1$ and $2$ is kept. Net force on third charge is directed toward original position if it is displaced along

1. equatorial line
2. axial line
3. None of these
4. Both $a$ and $b$

Q.

Three infinite long plane sheets carrying uniform charge densities
${\sigma }_1=-\sigma ,{\sigma }_2=+2\sigma$ and ${\sigma }_3=+3\sigma$ are placed parallel to the x-z plane at y =a, y=3a and y=4a as shown in Fig. 20.18. The electric field at point P is

1. zero

2. $-\frac{2\sigma }{{ϵ}_0}\hat{j}$

3. $-\frac{3\sigma }{{ϵ}_0}\hat{j}$

4. $\frac{3\sigma }{{ϵ}_0}\hat{j}$

Q. Two equal negative point charges $-q$ are fixed at points $(0,a)$ and $(0,-a)$ on the $\text{y-}$axis. A positive point charge $Q$ is in rest at point $(2a,0)$ on the $\text{x-}$axis. The net electric field on $Q$ due to both $-q$ charges will be $(\frac{1}{4\pi {ϵ}_0}=k)$

1. $\frac{qk}{a^2}$
2. $\frac{4qk}{5\sqrt{5}{a}^2}$
3. $\frac{4qk}{25a^2}$
4. $\frac{4qk}{3a^2}$

Q. A small block of mass $m$, charge $+q$ is kept at the top of a smooth inclined plane of angle ${30}^{\circ }$ placed in an elevator moving upward with an acceleration $a_0$.

Electric field $E$ exists between the vertical side walls of the elevator. The time taken by the block to come to the lowest point of inclined plane is (assuming the surface to be smooth).

1. $t=\sqrt{\frac{2h}{g}}$
2. $t=\sqrt{\frac{2h}{(g-a_0)+\frac{qE}{m}}}$
3. $t=2\sqrt{\frac{2h}{(g+a_0)-\frac{\sqrt{3}qE}{m}}}$
4. $t=\sqrt{\frac{2h}{(g+a_0{)}^2-\left(\frac{qE}{m}\right)h^2}}$

Q. Charges $2q$ and $-q$ are placed at $(a,0)$ and $(-a,0)$ as shown in the figure. The coordinates of the point at which electric field intensity is zero is $(x,0)$. Then:

1. $x>-a$
2. $-a<x<a$
3. $0<x<a$
4. $x<-a$

Q. A rod AB of length $L$ and mass $m$ is uniformly charged with a charge Q and it is suspended from end A as shown in the figure. The rod can freely rotate about A in the plane of figure. An electric field $E$ is suddenly switched on in the horizontal direction due to which rod gets turned by a maximum angle ${90}^o$. The magnitude of E is equal to $\frac{nmg}{Q}$. Find the value of n.

Q.

An electron is fixed at the origin as shown. What is the electric field at $\text{A}$?
(The coordinates are in metre)

1. $3.6\times {10}^{-19}\text{N/C}\hat{i}$
2. $-3.6\times {10}^{-10}\text{N/C}\hat{i}$
3. $3.6\times {10}^{-10}\text{N/C}\hat{i}$
4. None of these

Q. Find the electric at a point O.

1. $2\sqrt{2}\frac{kq}{a^2}$
2. $\sqrt{2}\frac{kq}{a^2}$
3. $\sqrt{3}\frac{kq}{a^2}$
4. $2\frac{kq}{a^2}$

Q. A particle of mass $m$ and charge $q$ enters with velocity $v_0$ perpendicular to a magnetic field B (coming out of the plane of the paper) as shown in the figure. It moves in the magnetic field for time $t=\frac{\pi m}{4qB}$, and then enters into a constant electric field region. The electric and magnetic fields are present only in a rectangular region of thickness $d$. The length of rectangular region is $l$. The particle enters parallel to and grazing the side $RQ$ and leaves the region at $P$.Given : $v_0=(\sqrt{2}+1)m{s}^{-1}$.
$\frac{E}{B}=8m{s}^{-1},l=\left|\frac{4\sqrt{2}}{5}{v}_0\right|$ metres and $\frac{m}{qB}=\frac{4}{5}$

Time taken by the particle to cross the electric field region is

1. $\frac{4}{5}s$
2. $\frac{3}{5}s$
3. $\frac{1}{5}s$
4. None of these

Q. A spherical conductor of radius $R$ carries charge $Q$ on its surface. The value of electric field just outside the surface of the conductor is $E$. If the radius of the counductor is doubled while keeping the charge same, what will be the value of new electric field just outside the surface of the conductor?

1. $E$
2. $2E$
3. $\frac{E}{4}$
4. $\frac{E}{2}$

Q. Electric field in a certain region is acting radially outward and the variation of electric field with distance from the origin is represented below. The slope of the graph is $A^{\prime }$.


The charge contained in a sphere of radius $a$ centred at the origin will be given by

1. $4\pi {ϵ}_0{A}^{\prime }{a}^2$
2. $\pi {ϵ}_0{A}^{\prime }{a}^2$
3. $8\pi {ϵ}_0{A}^{\prime }{a}^3$
4. $4\pi {ϵ}_0{A}^{\prime }{a}^3$

Q.

One can add electric field and gravitational field.

1. True

2. False

Q. $1\mu \text{C}$ charge is uniformly distributed on a spherical shell given by equation $x^2+y^2+z^2=25$. What will be the flux through an imaginary sphere of radius $3\text{m}$ and centre at origin ?

1. $25{\text{N-m}}^2/\text{C}$
2. $50{\text{N-m}}^2/\text{C}$
3. $5{\text{N-m}}^2/\text{C}$
4. Zero

Q.

The electric field in a region is given by
$E=(2\hat{i}+3\hat{j})\times {10}^{3}N{C}^{-1}$
The electric flux through a rectangular surface $10cm\times 20cm$ held parallel to the y-z plance is

1. $40N{C}^{-1}{m}^2$

2. $50N{C}^{-1}{m}^2$

3. $60N{C}^{-1}{m}^2$

4. zero