Question

A copper ball of density $p_c$ and diameter d is immersed in oil of density $p_o$ .What charge should be present on the ball , so that it could be suspended in the oil, if a homogeneous electric field E is applied vertically upward?

• A. Q = $\frac{\pi d^2(p_c-p_0)g}{6E}$
• B. Q = $\frac{\pi d^3(p_c-p_0)g}{6E}$
• C. Q = $\frac{\pi d^3(p_c-p_0)g}{E}$
• D. Q = $\frac{\pi d^2(p_c-p_0)g}{2E}$

Answer 1

The correct option is A Q = $\frac{\pi d^2(p_c-p_0)g}{6E}$

Copper ball of intensity $=P_C$ diameter $d$.

density $=P_0$

electric field $=E$

homogeneous electric field $E$ is applied Pressure

$P=hpg=\frac{(P_c-P_0)\times g\times \pi d^2}{6}$

Now,

$Q=\frac{P}{E}=\frac{\pi d^{2}g(P_c-P_0)}{6E}$