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Chapter 4: Q84P (page 719)

A small sphere with mass m carries a positive charge q and is attached to one end of a silk fiber of length L. The other end of the fiber is attached to a large vertical insulating sheet that has a positive surface charge density s. Show that when the sphere

is in equilibrium, the fiber makes an angle equal to arctan(蟽辩2蔚辞mg)with the vertical sheet.

Short Answer

Expert verified

Proven below

Step by step solution

01

Step 1:

Required: Proven that胃=arctan蟽辩2蔚辞mg

02

Figure

03

Calculation

The electric field of the infinite sheet is given by

E=蟽2蔚辞 (1)

So the force acting on the ball is given by

F=E=蟽辩2蔚辞 (2)

The electric force is equal to the tension component

Tsin(胃)=蟽辩2蔚辞 (3)

And the vertical component is equal to the weight

Tsin(胃)=mg (4)

Dividing (3) on (4) to get

tan(胃)=蟽辩2mg蔚辞鈬�胃=arctan蟽辩2蔚辞mg

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