Method of Images

Q. A point charge $Q_1=300\mu C$ is located at P(1, -1, -3) experiences an attractive force $\overrightarrow{F_1}=8\widehat{a_x}-8\widehat{a_y}+4\widehat{a_z}$ N due to point charge $Q_2$ at (3, -3, -2) m. The value of charge $Q_2$ will be

1. $-12\mu C$
2. $-40\mu C$
3. $-36\mu C$
4. $-20\mu C$

Q. In a source free region in vacuum, if the electrostatic potential $\varphi =4x^2+y^2+c{z}^2$, the value of constant c will be

1. 2
2. -3
3. -5
4. 4

Q. Two conducting plate are inclined at an angle ${30}^{\circ }$ to each other with a point charge between them. The number of image charges are

1. 12
2. 11
3. 5
4. 6

Q. An electrostatic field is said to be conservative when:

1. The divergence of the field is equal to zero
2. The curl of the field is equal to zero
3. The curl of the field is equal to $-\frac{\partial E}{\partial t^2}$
4. The Laplacian of the field is equal to $\mu \epsilon \frac{{\partial }^{2}E}{\partial t^2}$

Q. If the potential given by $\overrightarrow{V}=\frac{20sin\theta }{r^3}$ in a region, then value of volume charge density ${\rho }_v$ at point $P(r=2,\theta ={30}^{\circ },\varphi =0^{\circ })$ will be

1. $84.21pC/m^3$
2. $-20.24pC/m^3$
3. $80.42pC/m^3$
4. $-22.12pC/m^3$