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 10−4A. What is the surface density of charge on the belt?

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

Solution

## The correct option is C 6.7×10−4Cm−2Let 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 10−4=σ×0.3×0.5 ⇒σ=6.67×10−4 Cm−2≈6.7×10−4 Cm−2Physics

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