198Chapt. 25Electric Potentialthe charge to flow to the dome. The charge can be positive (absence of electrons) or negative(excess of electrons). We assume positive for definiteness in this problem.a) Say the belt conveys a constant net current (charge per unit time) ofIto the dome. Whatis the formula for timetfor charge on the dome to reachqwhen it started at zero?b) Say the chargeqends up uniformly spread over the outer surface of the dome which wecan approximate to high accuracy as spherical shell of radiusR. Let the radial coordinateber.Assuming exact spherical symmetry, what are the formulae for theELECTRICFIELDandELECTRICAL POTENTIALforr≥R?HINT:General formulae arenot acceptable answers. What are the formulae for this specific case.c) The Van de Graaff generator is a neat trick to build up net charge. But in building upnet charge, one also builds up potential energy in the distribution of charge on the dome’ssurface. But you don’t get things for free. By what process done by what component of
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