he electric field between the plates of a parallel plate capacitor is horizontal, uniform, and has a magnitude E. A small object mass 0.0250 kg and charge -3.10

Question

The electric field between the plates of a parallel plate capacitor is horizontal, uniform, and has a
magnitude E. A small object mass 0.0250 kg and charge -3.10 µC is suspended in the field by a
thread as shown below. The thread makes an angle of 10.5 degrees with the vertical.

a. What is the tension in the thread? (ans: a. 0.249 N)
b. What is the magnitude of the electric field? (ans: 1.46 x 104 N/C)

Answer 1

(a)

 

The electric force is strictly horizontal in this problem, so

 

T cosθ = mg ⇒

 

T = mg/cosθ = (0.0250)(9.8)/cos10.5° ≅ 0.249 N

 

(b)

 

The charge is attracted to the positive plate by a force qE in equilibrium with the horizontal component of the tension.

 

qE = T sinθ ⇒

 

|E| = T sinθ / |q| = (0.249 N) sin10.5° / (3.10 x 10^-6 C) ≅ 1.46 x 10⁴ N/C