Two non-conducting infinite plane sheets A and B have surface charge densities K σ and σ respectively. A metallic ball of mass m and charge +q is attached to a thread and the thread is tied at point P

Question

Two non-conducting infinite plane sheets A and B have surface charge densities $K σ$ and $σ$ respectively. A metallic ball of mass m and charge +q is attached to a thread and the thread is tied at point P on sheet A. Initially ball is in equilibrium at point P when sheets are uncharged. Find the CORRECT option. (K is a constant)

TestHub · Accepted Answer

For K > 1, the net field between the sheets is $E = \frac{K σ - σ}{2 ε _{0}} = \frac{( K - 1 ) σ}{2 ε _{0}}$ , pointing away from sheet A.

Equilibrium of the ball: $tan θ = \frac{qE}{m g} = \frac{( K - 1 ) σ q}{2 ε _{0} m g}$ .

Hence (D). (For K = 1 the field is zero, so $θ = 0$ , not 45°.)

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