Idea of Symmetry

Q. 14.Plot the graph showing the variation of coloumb force versus 1r2 where r is the distance between the two charges of each pair of charges 1 microcolumb , 2 microcolumb & 1 microcolumb, -3microcolumb interpret the graph obtained & explain as well

Q. A point charge q is placed at a distance $\frac{a}{2}$ directly above the centre of a square of side a. The electric flux through the square is

1. $\frac{q}{{ϵ}_0}$
2. $\frac{q}{\pi {ϵ}_0}$
3. $\frac{q}{4{ϵ}_0}$
4. $\frac{q}{6{ϵ}_0}$

Q. If the electric field is given by 3i+2j+6k . Find the electric flux through a surface area 20unit lying in xy plane.

Q.

Is electric force the opposite in direction of electric field?

Q.

The electric field in a region is given by $\overrightarrow{E}=\frac{2}{5}{E}_{\circ }\hat{i}+\frac{3}{5}{E}_{\circ }\hat{j}$ with $E_{\circ }=4.0\times {10}^{3}N/C$.The flux of this field through a rectangular surface are $0.4m^2$parallel to Y–Z plane is________$N{m}^2{C}^{-1}$.

Q. If a charge $q$ is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be:

1. $\frac{q}{2\pi {\epsilon }_0}$
2. $\frac{q}{4{\epsilon }_0}$
3. $\frac{q}{2{\epsilon }_0}$
4. $\frac{q}{{\epsilon }_0}$

Q.

SI unit of permittivity is:

Q. A charge Q is uniformly distributed over a rod of length 2l. Consider cube of edge l with the centre of cube at one end of the rod.The minimum possible electric flux through the surface of the cube is

Q.

The electric field at a point is

1. Always continuous

2. Continuous if there is no charge at that point

3. Discontinuous if there is a charge at that point

4. Both (B) and (C) are correct

Q. Electric potential existing in space is given by $V=K(x^{2}y+y^{2}z+xyz)$. Find the expression for electric field.

1. $0$
2. $-K\{(2xy+yz)\hat{i}+(x^2+2yz+xz)\hat{j}+(y^2+xy)\hat{k}\}$
3. $-K\{[\frac{x^{3}y}{3}+\frac{x^{2}yz}{2}]\hat{i}+(y^2+xy)\hat{k}\}$
4. $K\{[2xy+yz]\hat{i}+[x^2+2yz+xy]\hat{j}+(y^2+xy)\hat{k}\}$

Q. Two pith balls each of mass M and charge Q are suspended from a point by weightless threads of length L. Both the Threads are separated by an angle theta with the vertical. The theta is small, the distance between two pith balls will be??

Q.

What is the shape of equipotential surfaces for an isolated point charge?

Q.

How is energy stored in an electric field?

Q. A charge q is located at the centre of a cube. The electric flux through any face of the cube is

Q.

Why electric field strength in a sphere is zero?

Q. A ring of uniform charge with radius 0.5 m having a 0.02 m gap, carries a charge +1C. The electric field at the centre is:

1. $2.31\times {10}^{4}N/C$
2. $2.31\times {10}^{8}N/C$
3. $1.6\times {10}^{4}N/C$
4. $1.6\times {10}^{8}N/C$

Q. A certain charge $Q$ is to be divided into two parts $q$ and $Q-q$. The relationship between $Q$ and $q$ placed at a certain distance apart to have the maximum Coulomb repulsion is

1. $q=\frac{Q}{2}$
2. $q=\frac{Q}{3}$
3. $q=\frac{2Q}{2}$
4. $q=\frac{Q}{4}$

Q. Why can't Gauss law be used to calculate the field distribution around an electric dipole?

Q.

Resistance has the same dimensions as, where h is the Plancks constant and e is the charge.

1. ${\mathrm{h}}^2/{\mathrm{e}}^2$

2. ${\mathrm{h}}^2/\mathrm{e}$

3. $\mathrm{h}/{\mathrm{e}}^2$

4. $\mathrm{h}/\mathrm{e}$

Q.

When ${10}^{19}$electrons are removed from a neutral metal plate through some process, the charge on it becomes _____?

Q.

A uniform magnetic field B exists in the region between $x=0$ and $x=\frac{3R}{2}$ (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge $+Q$ and momentum $p$ directed along x-axis enters region 2 from region 1 at point $P_1(y=-R)$. Which of the following option(s) is/are correct?

1. For $B=\frac{8}{13}\frac{p}{QR}$, the particle will enter region 3 through the point $P_2$ on x-axis

2. For $B>\frac{2}{3}\frac{p}{QR}$, the particle will re-enter region 1

3. When the particle re-enters region 1 through the longest possible path in region 2, the magnitude of the change in its linerar momentum between point $P_1$ and the farthest point from y-axis is $p/\sqrt{2}$

4. For a fixed B, particles of same charge Q and same velocity $v$, the distance between the point $P_1$ and point of re-entry region 1 is inversely proportional to the mass of the particle

Q. Consider a cube of side $a=0.1m$ placed such that its six faces are given by equation $x=0,x=+a,y=0,y=+a,z=0$ and $z=+a$. If its placed in a electric field given by $\overrightarrow{E}=x^2\hat{i}+y\hat{j}$ N/C, the electric flux crossing out of the cube in the unit of ${10}^{-4}N{m}^2/C$ is

Q.

A cube of side b has a charge q at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.

Q. A cube of side $a$ is placed such that the nearest face which is parallel to the y-z plane, is at a distance $a$ from the origin. The electric field components are $E_x=\beta x^{1/2},E_y=E_z=0$.
The charge within the cube is

1. $\sqrt{2}\beta {ϵ}_a{a}^{5/2}C$
2. $(\sqrt{2}-1)\beta {ϵ}_o{a}^{5/2}C$
3. $-\beta {ϵ}_o{a}^{5/2}C$
4. zero

Q.

In electric flux taken in sphere the electric field and area are taken in same direction when a q positive charge is taken at centre the angle between electric field and the area is 0 then dot product of their will zero or not

Q.

Gauss law and it's application

Q. Two charges of magnitudes -2Q and +Q are located at points (a, 0) and (4a, 0) respectively. What is the electric flux due to these charges through a sphere of radius '3a' with its center at the origin?

Q. a region of space contains a constant electric field of magnitude 1325 N/C .A wire frame forming a square of 0.27m on a side is placed in this region.Oriented so that the perpendicular to the square makes an angle of 48 with the field. What is the magnitude of electric flux through the frame?

Q. The surface charge density of a hollow hemisphere varies with $\theta$ as $\sigma ={\sigma }_0\cos \theta$. The situation is shown in the figure. Find the total charge on the hemisphere.

1. $\frac{{\sigma }_0\pi R^2}{2}$
2. $2{\sigma }_0\pi R$
3. ${\sigma }_0\pi R^2$
4. ${\sigma }_0\pi R^3$

Q. Find the current in a copper wire having cross-sectional area $2{\text{mm}}^2$. Given that Electric field $E=8.5\times {10}^{-3}\text{V}{\text{m}}^{-1}$ and resistivity $\rho =1.7\times {10}^{-8}\Omega \text{m}$

​​​​​​​$[$1 Mark$]$

1. $1\text{A}$
2. $3\text{A}$
3. $2\text{A}$
4. $4\text{A}$