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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(σq2εomg)with the vertical sheet.

Short Answer

Expert verified

Proven below

Step by step solution

01

Step 1:

Required: Proven thatθ=arctanσq2εomg

02

Figure

03

Calculation

The electric field of the infinite sheet is given by

E=σ2εo (1)

So the force acting on the ball is given by

F=E=σq2εo (2)

The electric force is equal to the tension component

Tsin(θ)=σq2εo (3)

And the vertical component is equal to the weight

Tsin(θ)=mg (4)

Dividing (3) on (4) to get

tan(θ)=σq2mgεo⇒θ=arctanσq2εomg

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