A simple pendulum has a bob of mass m and charge q. The pendulum string has negligible mass. When a uniform horizontal electric field ⃗E is applied, the tension in the string changes. The final tension in the string, when the pendulum attains its equilibrium position, is . (g is the acceleration du…

Question

A simple pendulum has a bob of mass m and charge q. The pendulum string has negligible mass. When a uniform horizontal electric field ⃗E is applied, the tension in the string changes. The final tension in the string, when the pendulum attains its equilibrium position, is . (g is the acceleration due to gravity)

Accepted Answer

(3) √m²g²+q²E². At equilibrium the string hangs at some angle θ to the vertical, and three forces act on the bob: the weight mg down, the electric force qE horizontal, and the tension T along the string. Resolving: T cos θ=mg and T sin θ=qE. Squaring and adding, T²(cos²θ+sin²θ)=m²g²+q²E². T=√m²g²+q²E², which is larger than mg: the field always tightens the string. (The angle follows from tan θ=(qE)/(mg).)

Step-by-step solution

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