   Chapter 16, Problem 36P

Chapter
Section
Textbook Problem

A small object with a mass of 350. μg carries a charge of 30.0 nC and is suspended by a thread between the vertical plates of a parallel-plate capacitor. The plates are separated by 4.00 cm. If the thread makes an angle of 15.0° with the vertical, what is the potential difference between the plates?

To determine
The potential difference between the plates.

Explanation

Given info: The mass of the object is 350μg . The charge on the object is 30.0 nC. The distance of separation is 4.00 cm.

Explanation:

The free body diagram is,

• Fe is the electric force.
• T is the tension.
• m is the mass of the object.
• g is the acceleration due to gravity.

From the diagram,

Tcos15ο=mg

Tsin15ο=Fe

Dividing the 2nd equation by the 1st,

Fe=mgtan15ο

Formula to calculate the electric force is,

Fe=qVd

• V is the electric field.
• q is the charge on the ball.
• d is the distance between the plates.

Therefore,

qVd=mgtan15ο

On Re-arranging,

V=mgdtan15οq

Substitute 9.8ms2 for g, 30

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