Properties of Field Lines

Q.

(a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?

(b) Explain why two field lines never cross each other at any point?

Q. two point charges of 5μ c and 20 μ c are separated by a dis†an ce of 2 m. find the point on the line joining them at which electric field intensity is zero

Q.

What is the dimension of magnetic induction?

Q. Why do the electrostatic field lines not form closed loops?

Q. Three identical charges of charge $q$ are placed at the three corners of an equilateral triangle. The electric potential $V$ and the intensity of the electric field $E$ at the centroid $\text{O}$ will be

1. $V=0$ , $E\ne 0$
2. $V\ne 0$ , $E=0$
3. $V\ne 0$ , $E\ne 0$
4. $V=0$ , $E=0$

Q. Two point charges Q and -3Q are placed some distance apart. If the electric field at the location of Q is E, find the electric field at the location of -3Q.

Q.

At which point or points is the electric field zero

Q. A parallel plate capacitor has a uniform electric field $\overrightarrow{E}$ in the space between the plates. If the distance between the plates is $d$ and the area of each plate
is $A,$ the energy stored in the capacitor is
(${\epsilon }_0=$ permittivity of free space)

1. $\frac{E^{2}Ad}{{\epsilon }_0}$
2. $\frac{1}{2}{\epsilon }_0{E}^2$
3. ${\epsilon }_{0}EAd$
4. $\frac{1}{2}{\epsilon }_0{E}^{2}Ad$

Q. Three charges each of magnitude $q$ are placed at the vertices of an equilateral triangle having side $l$. The electrostatic force on an identical charge placed at the centroid of the triangle is

1. Zero
2. $\frac{1}{4\pi {ϵ}_o}\frac{q^2}{l^2}$
3. $\frac{1}{4\pi {ϵ}_o}\frac{3q^2}{l^2}$
4. $\frac{1}{12\pi {ϵ}_o}\frac{q^2}{l^2}$

Q. Find the flux through the curved surface of a given cylindrical Gaussian surface around a point charge $+9\text{nC}$ kept at centre at the axis.
(Take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$)

1. $300\sqrt{3}{\text{N-m}}^2\text{/C}$
2. $400\sqrt{3}{\text{N-m}}^2\text{/C}$
3. $500\sqrt{3}{\text{N-m}}^2\text{/C}$
4. $600\sqrt{3}{\text{N-m}}^2\text{/C}$

Q. 3 point charges q, 2q, 8q are to be placed along a 9cm long straight line.find the positions where the charges should be placed such that potential energy of this system is minimum .in this situation, what is the electric field at q due to other two charges??

Q. The electric force on a charge $q_1$ due to $q_2$ is $(4\hat{i}-3\hat{j})\text{N}$. The unit vector in the direction of electirc force on $q_2$ due to $q_1$ will be:

1. $-4\hat{i}+3\hat{j}$
2. $\frac{-4}{5}\hat{i}+\frac{3}{5}\hat{j}$
3. $-\frac{4}{5}\hat{i}-\frac{3}{5}\hat{j}$
4. $\frac{4}{5}\hat{i}+\frac{3}{5}\hat{j}$

Q. The figure shows some of the electric field lines corresponding to an electric field. The figure suggests

1. $E_A>E_B>E_C$
2. $E_A=E_B=E_C$
3. $E_A=E_C>E_B$
4. $E_A=E_C<E_B$

Q.

A dipole is placed parallel to the electric field. If W is the work done in rotating the dipole by ${60}^o$, then the work done in rotating it by 180º is

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

Q. Consider a system of three charges $\frac{q}{3},\frac{q}{3}$ and $\frac{-2q}{3}$ placed at points A, B and C respectively as shown in the figure. Take O to be the centre of the circle of radius $R$ and angle $CAB={60}^{\circ }$. Then, which of the following option(s) is/are correct?

1. The electric field at point O is $\frac{q}{8\pi {\in }_0{R}^2}\hat{i}$.
2. The magnitude of the force between the charges at C and B is $\frac{q^2}{54\pi {\in }_0{R}^2}$.
3. The potential energy of the system is zero.
4. The potential at point O is $\frac{q}{12\pi {\in }_{0}R}$.

Q. For the given spherical Gaussian surface around and centred at infinite positive line charge, the angle between electric field $\overrightarrow{E}$ and area vector $\overrightarrow{A}$, at all the point on the surface is

1. equal but not $0^{\circ }$ or ${90}^{\circ }$
2. not equal
3. $0^{\circ }$
4. ${90}^{\circ }$

Q. An electric dipole of length $10\text{cm}$ having charges $6\times {10}^{-3}\text{C}$ is placed at ${60}^{\circ }$ with respect to a uniform electric field. If it experiences a torque of $3\sqrt{3}\text{N-m}$, then the magnitude of electric field is

1. $1\times {10}^4\text{N/C}$
2. $2\times {10}^4\text{N/C}$
3. $3\times {10}^4\text{N/C}$
4. $4\times {10}^4\text{N/C}$

Q. Oэь/bbEight point charges (can be assumed as small spheres uniformlycharged and their centres at the corner of the cube) having values qb9-6Aeach are fixed at vertices of a cube. The electric flux through squaresurface ABCD of the cube isbb(D) 8EOPage # 1b(C) 6 EOb(B) 12 Eo(A) 24 Eo

Q. Q 12/60 Positive and negative charge in 18 cc of water is

Q.

The magnetic field interacts with the

1. Stationary charge only

2. Moving charges only

3. Stationary and moving charges

4. Neither stationary nor moving charges

Q. For the given uniformly charged ring, what will be the maximum value of electric field?

1. $116\text{N/C}$
2. $126\text{N/C}$
3. $136\text{N/C}$
4. $146\text{N/C}$

Q. For a uniformly charged ring of radius $R$, the electric field on its axis has the largest magnitude at a distance $h$ from its centre. Then the value of $h$ is:

1. $R$
2. $\frac{R}{\sqrt{5}}$
3. $\frac{R}{\sqrt{2}}$
4. $R\sqrt{2}$

Q. A circular wire loop of radius $R$ is placed in the $XY-$plane, centered at the origin $O$. A square loop of side $a$ $(a<<R)$ having two turns is placed with its center at $Z=\sqrt{3}R$ along the axis of the circular wire loop as shown in figure. The plane of the square loop makes an angle of ${45}^{\circ }$ with respect to the $Z-$axis. If the mutual inductance between the loops is given by $\frac{{\mu }_0{a}^2}{2^{P/2}R}$, then the value of $P$ is -

1. $3$
2. $4$
3. $5$
4. $7$

Q. A wire is bent into a semicircular arc of radius R. The rod has a uniform linear charge distribution x. The potential at the centre is?

Q. (a) Deduce the expression for the torque acting on a dipole of dipole moment $\overrightarrow{p}$ in the presence of a uniform electric field $\overrightarrow{E}$.

(b) Consider two hollows concentric spheres, $S_1$ and $S_2$, enclosing charges 2Q and 4Q respectively as shown in the figure. (i) Find out the ratio of the electric flux through them. (ii) How will the electric flux through the sphere $S_1$ change in a medium of dielectric constant ${}^{\prime }{\epsilon }_r^{\prime }$ if ${}^{\prime }{\epsilon }_r^{\prime }$ is introduced in the space inside $S_1$ in place of air?

Deduce the necessary expression.

Q.

If $E_A,E_B,E_{C}and{E}_D$ represent the magnitudes of electric fields at A, B, C and D. Which of the options are correct?

1. E_A > E_B > E_D > E_C

2. E_A < E_B < E_D < E_C

3. E_A > E_B > E_C > E_D

4. E_A < E_B < E_C < E_D

Q. Two large parallel planes charged uniformly with surface charge density $\sigma$ and $-\sigma$ are located as shown in the figure. Which one of the following graphs shows the variation of electric field along a line perpendicular to the planes as one moves from A to B ?

1. 
2. 
3. 
4. 

Q. Assume that and electric field $\underset{E}{\to }=30x^{2}i$ exists is space. Then the potential difference $V_A–V_0$ is:
(where $V_0$ is the potential at the origin and $V_A$ is the potential at x = 2m)

1. 80 V
2. 120 V
3. -120 V
4. -80 V

Q. The electric field intensity near to surface of charged conductor
A. Is directed along the surface
B. is directed normal to the surface
C. depends upon local radius of curve
D. depends upon surface charge density at the point

1. A, B
2. A, C
3. A, D
4. B, C, D