A copper wire of diameter d is immersed in an oil of density rho not. There is a uniform electric field E directed vertically upwards such that the copper ball remains just suspended in the oil. Density of copper is rho c. The charge on the ball is ?

Dear Student,

I think the copper ball not the copper wire in the first statement.

Please find below the solution to the asked query:

Here, the copper ball weight acts in the downward direction and the bouncy force and the force due to Electric Field acts in the upward direction.

Let the charge on the copper ball is q, then

$W={F}_{B}+{F}_{E}⇒mg=V{\rho }_{0}g+qE\phantom{\rule{0ex}{0ex}}⇒V{\rho }_{C}g=V{\rho }_{0}g+qE⇒qE=V{\rho }_{C}g-V{\rho }_{0}g\phantom{\rule{0ex}{0ex}}⇒q=\frac{V\left({\rho }_{c}-{\rho }_{0}\right)g}{E}$

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