An electric field E⃗ =(2.30×10^5 N/C, right) causes a 2.0 g ball to hang at an angle. If the ball carries a charge q = 25 nC, what is the angle θ between the string and the vertical?

• A. 10 degrees
• B. 16.4 degrees
• C. 30 degrees
• D. 45 degrees

Answer: (B)

The key idea is that a charged pendulum in an electric field experiences a horizontal electric force that shifts the vertical balance point, so the tension in the string has components that balance both the horizontal electric force and the vertical weight. At equilibrium, the horizontal component of the string’s tension must equal the electric force qE, while the vertical component must balance the weight mg. This gives tan θ = (qE) / (mg).

Compute the forces: qE = (25 × 10^-9 C)(2.30 × 10^5 N/C) = 5.75 × 10^-3 N. The weight is mg = (0.002 kg)(9.8 m/s^2) = 0.0196 N. Therefore tan θ = 0.00575 / 0.0196 ≈ 0.293, so θ ≈ arctan(0.293) ≈ 16.4 degrees.