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Chapter 4: Q33P (page 747)

A small sphere with mass 4.00×10-6 kgand charge 5.00×10-8Changs from a thread near a very large, charged insulating sheet (Fig.P22.33). The charge density on the surface of the sheet is uniform and equal to -2.50×10-9C/m2. Find the angle of the thread.

Short Answer

Expert verified

The angle of the thread is 10.2°

Step by step solution

01

Define free body diagram and given data

Free body diagram,

Given,

m=4×10-6kgσ=2.50×10-9C×m-2q=5.0×10-8C

02

Simplify the direction of force

The ball is in equilibrium so the net force in each direction is equal to zero so the force indirection is given by

Tsin(θ)=Fe ......(1)

Also, the force in y direction is

Tcosθ=mg....2

Dividing (1) over (2) to get

tan(θ)=Femg Þ(3)

The electric force is given by

Fe=Eq=qσ2o0'=2.5×10-9×5×10-82×8.85×10-12=7.06×10-6N

Also, the gravitational force is given by

mg=4×10-6×9.8=3.9×10-5N

Substitution in (3) to get

tanθ=7.06×10-63.9×10-5=0.18θ=10.2°

Hence, the angle of the thread is 10.2°

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