Question

A pendulum bob of mass 70 mg and carrying a charge of 40 nC is at rest in a horizontal

uniform electric field of strength 30, 000 NC-1
. Find the tension in the thread of the

pendulum and the angle it makes with the vertical.​

Answer 1

Given : A pendulum bob of mass 70 mg and carrying a charge of 40 nC is at rest in a horizontal uniform electric field of strength 30000 N/C.

To find : The tension in the thread of the pendulum and the angle it makes with the vertical.

solution : see figure, Here tension in the thread of the pendulum is T and angle makes with the vertical is θ.

for vertical components

Tcosθ = mg .......(1)

for horizontal components

Tsinθ = qE ......(2)

from equations (1) and (2) we get,

T = √{(mg)² + (qE)²} and tanθ = qE/mg

here, m = 70 mg = 70 × 10^-6 Kg = 7 × 10^-5 kg

q = 40nC = 40 × 10^-9 C = 4 × 10^-8 C

E = 30000 = 3 × 10⁴ N/C

g = 10 m/s²

so, tension in the thread, T = √{(7 × 10^-5 × 10)² + (4 × 10^-8 × 3 × 10⁴)²}

= √{(7 × 10¯⁴)² + (12 × 10¯⁴)²}

= √{49 + 144} × 10¯⁴ N

= 13.89 × 10¯⁴ N

angle makes with the vertical, θ = tan¯¹ [qE/mg]

= tan¯¹[12 × 10¯⁴/7 × 10¯⁴ ]

= tan¯¹ (12/7)

≈ 59.74°

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