Question

A small object with charge q and weight mg is attached to one end of a string of length ‘L’ attached to a stationary support. The system is placed in a uniform horizontal electric field ‘E’, as shown in the accompanying figure. In the presence of the field, the string makes a constant angle θ with the vertical. The sign and magnitude of q ______.

Options

• positive with magnitude mg/E

• positive with magnitude (mg/E)tanθ

• negative with magnitude mg/E tanθ

• positive with magnitude E tanθ/mg

Answer 1

A small object with charge q and weight mg is attached to one end of a string of length ‘L’ attached to a stationary support. The system is placed in a uniform horizontal electric field ‘E’, as shown in the accompanying figure. In the presence of the field, the string makes a constant angle θ with the vertical. The sign and magnitude of q positive with magnitude (mg/E)tan θ.

Explanation:

F_e = mg tan θ

qE = mg tan θ

q = `("mg"/"E")`tan θ

tan θ = `"F"_"e"/"mg"`