Surface Integral

Q. Electric flux through both the sides of a surface is equal.

1. False
2. True

Q. Charge Q is placed inside cone as shown in figure such that $\theta ={60}^{\circ }$. Flux of electric field associated with curved surface of cone is.

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

Q. A long string with a charge of $\lambda$ per unit length passes through an imaginary cube of edge $l$. The maximum possible flux of the electric field through the cube will be

1. $\frac{\sqrt{2}\lambda l}{{ϵ}_0}$
2. $\frac{6\lambda l^2}{{ϵ}_0}$
3. $\frac{\sqrt{3}\lambda l}{{ϵ}_0}$
4. $\frac{\lambda l}{{ϵ}_0}$

Q. Consider an infinite line charge having uniform linear charge density and passing through the axis of a cylinder. What will be the effect on the flux passing through the cylinder if the portions of the line charge outside the cylinder is removed.

1. decreases
2. increases
3. remains same
4. cannot say

Q.

In a region where intensity of electric field is $5N{C}^{-1}$ , $40$ lines of electric force are crossing per square metre. The number of lines crossing per square metre where intensity of electric field is $10N{C}^{-1}$ will be :

1. $20$
2. $100$
3. $80$
4. $200$

Q. Change $Q_1$ and $Q_2$ lie inside and outside respectively of a closed surface $S$. Let $E$ be the field at any point on $S$ $\varphi$ be the flux of $E$ (electric field) over $S$.

	List-I		List-II
(P)	If $Q_1=0$ and $Q_2\ne 0$ then	(1)	Both $E$ and $\varphi$ will change
(Q)	If $Q_1\ne 0$ and $Q_2=0$ then	(2)	$E\ne 0$ and $\varphi \ne 0$
(R)	If $Q_2$ changes	(3)	net electric field will change but $\varphi$ will not change
(S)	If $Q_1$ changes	(4)	$E\ne 0$ but $\varphi =0$

1. P - 4, Q - 2, R - 3, S - 1
2. P - 1, Q - 2, R - 4, S - 3
3. P - 2, Q - 4, R - 1, S - 3
4. P - 3, Q - 4, R - 1, S - 2

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

1. $\frac{\pi q}{6\left(4\pi {\epsilon }_0\right)}$
2. $\frac{q}{6\left(4\pi {\epsilon }_0\right)}$
3. $\frac{4\pi q}{6\left(4\pi {\epsilon }_0\right)}$
4. $\frac{4\pi q}{\frac{1}{6}\left(4\pi {\epsilon }_0\right)}$

Q. Calculate the net flux emerging from given enclosed surface $-{Nm}^2{C}^{-1}$

1. $4.5\times {10}^{11}$
2. $45\times {10}^{12}$
3. zero
4. $1.12\times {10}^{12}$

Q. The electric flux passing through a hemispherical surface of radius R placed in an electric field E with its axis parallel to the filed is :

1. $\pi R^{2}E$
2. $2\pi R^{2}E$
3. $2\pi RE$
4. $2\pi R^{3}E$

Q. A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by :

1. $\frac{R}{E}$
2. $2\pi R^{2}E$
3. $\frac{\pi R^2}{E}$
4. Zero