EXERCISES

What is the force between two small charged sphere having charges of $2\times {10}^{-7} \mathrm{C}$ and $3\times {10}^{-7} \mathrm{C}$ placed $30 \mathrm{cm}$ apart in air? ($k = 9\times {10}^9 {\mathrm{Nm}}^2{\mathrm{C}}^{-2}$)

The electrostatic force on a small sphere of charge $0.4 \mathrm{\mu }\mathrm{C}$ due to another small sphere of charge $–0.8 \mathrm{\mu }\mathrm{C}$ in the air is $0.2 \mathrm{N} .$ What is the distance between the two spheres? ($k = 9\times {10}^9 {\mathrm{Nm}}^2{\mathrm{C}}^{-2}$)

The electrostatic force on a small sphere of charge $0.4 \mathrm{\mu }\mathrm{C}$ due to another small sphere of charge $–0.8 \mathrm{\mu }\mathrm{C}$ in the air is $0.2 \mathrm{N}.$
What is the force on the second sphere due to the first?

Four-point charges ${\mathrm{q}}_{\mathrm{A}}=2 \mathrm{\mu }\mathrm{C}, {\mathrm{q}}_{\mathrm{B}}=–5 \mathrm{\mu }\mathrm{C}, {\mathrm{q}}_{\mathrm{C}}=2 \mathrm{\mu }\mathrm{C},\mathrm{and} {\mathrm{q}}_{\mathrm{D}}=–5 \mathrm{\mu }\mathrm{C}$ are located at the corners of a square $\mathrm{ABCD}$ of side $10 \mathrm{cm}$. What is the force on a charge of $1 \mathrm{\mu }\mathrm{C}$ placed at the center of the square?

Two point charges $q_A=3 \mathrm{\mu }\mathrm{C}$ and  $q_{B }=-3 \mathrm{\mu C}$ are located $20 \mathrm{cm}$ apart in vacuum. What is the electric field at the midpoint $\mathrm{O}$ of the line $\mathrm{AB}$ joining the two charges? If a negative test charge of magnitude $1.5\times {10}^{-9} \mathrm{C}$ is placed at this point, what is the force experienced by the test charge? Take, $\frac{1}{4\pi {\in }_0}=9\times {10}^9 {\mathrm{Nm}}^2{\mathrm{C}}^{-2}$

A uniformly charged conducting sphere of $2.4 \mathrm{m}$ diameter has a surface charge density of $80 \mathrm{\mu C}/{\mathrm{m}}^2$. Find the charge on the sphere. What is the total electric flux leaving the surface of the sphere?

An infinite line charge produces a field of  $9\times {10}^4 \frac{\mathrm{N}}{\mathrm{C}}$ at a distance of  $2 \mathrm{cm}$. Calculate the linear charge density. Take, ${\in }_0 = 8.854\times {10}^{-12} {\mathrm{C}}^2/\mathrm{N}.{\mathrm{m}}^2$

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17\times {10}^{-12} \mathrm{C}/{\mathrm{m}}^2$. What is $E$: a) in the outer region of the first plate b) in the outer region of the second plate and c) between the plates? Take, ${\in }_0=8.854\times {10}^{-12} {\mathrm{N}}^{-1}{\mathrm{C}}^2 {\mathrm{m}}^{-2}$.