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Question 26.3: A charged belt, 50 cm wide, travels at 30 m/s between a sour......

A charged belt, 50 cm wide, travels at 30 m/s between a source of charge and a sphere. The belt carries charge into the sphere at a rate corresponding to 100 μA. Compute the surface charge density on the belt.

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We adapt the discussion in the text to a moving two-dimensional collection of charges. Using σ for the charge per unit area and w for the belt width, we can see that the transport of charge is expressed in the relationship i = σνw, which leads to

\sigma=\frac{i}{ν w}=\frac{100 \times 10^{-6} \,A }{(30 \,m / s )\left(50 \times 10^{-2} \,m \right)}=6.7 \times 10^{-6} \,C / m ^2 .

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