Question

A ball of mass 2 mg carrying a charge of 4x10-C is
hanging vertically by a thread. When a large metal plate
is brought nearer to the ball, the thread makes an angle
30° with vertical. The surface charge density of the plate is .,​

Answer 1

Answer:Hope it helps :)

Explanation:A small sphere of mass m and charge q is hung from silk thread at angle θ with the surface of a vertical charge conducting plate as shown in figure.

We know, Electric field intensity act due to plate = σ/ε₀, where σ is surface charge density of plate.

At equilibrium ,

Upward force = downward force

Tcosθ = mg ----(1)

Forward force = backward force

Tsinθ = σq/ε₀ [ ∵ F = qE , ∴ F = qσ/ε₀ ] -----(2)

Dividing equation (2) by (1)

Tsinθ/Tcosθ = qσ/ε₀mg

⇒Tanθ = qσ/ε₀mg

σ = ε₀mg tanθ/q

Hence, surface charge density of plate is σ = ε₀mg tanθ/q

Answer 2

Explanation:

We know that,

Electric field intensity act due to plate =

where , σ = surface charge density of plate

At equilibrium,

Upward force = downward force