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Question

The belt of an electrostatic generator is 50cm wide and travels 30cm/s. The belt carries charge into the sphere at a rate corresponding to 104A. What is the surface density of charge on the belt?


A
6.7×105Cm2
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B
6.7×107Cm2
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C
6.7×104Cm2
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D
6.7×108Cm2
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Solution

The correct option is C 6.7×104Cm2
Let the surface charge density of the belt be σ.
Velocity of the belt, V=30 cm/s=0.3 m/s
Width of the belt, w=50 cm=0.5 m
Since surface charge density, σ=QA
Q=σ×A
Dividing both sides by time t
Qt=σ×At(1)
Since Qt=I and A=l×w
where l is the length of the belt
At=l×wt=V×w
Therefore equation (1) becomes,
I=σ×V×w
104=σ×0.3×0.5
σ=6.67×104 Cm26.7×104 Cm2

Physics

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