Question

A copper ball of density $8.6\, g cm ^{-3}, 1 \,cm$ in diameter is immersed in oil of density $0.8 \,g cm ^{-3}$. If the ball remains suspended in oil in a uniform electric field of intensity $36000\, NC ^{-1}$ acting in upward direction, what is the charge on the ball?

• A. $1.1\, \mu C$
• B. $4.2\, \mu C$
• C. $2.4\, \mu C$
• D. $3.7 \,\mu C$

Answer 1

Answer: (A)

Apparent weight of the ball $=m g-$ upthrust
$=\frac{4}{3} \pi r^{3}(\rho-\sigma) g=\frac{4}{3} \pi \times(0.5)^{3} \times(8.6-0.8) \times 980$
$=4,002.4$ dyne $=4.0024 \times 10^{-2} N$
Let $q$ be the charge on the ball. As the ball remiand suspended,
$q E=$ apparent weightl of the ball
or $q=\frac{\text { apparent weight }}{E}=\frac{4.0024 \times 10^{-2}}{36,000}$
$ = 1.11 \times 10^{-6} C$