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The potential at the centre of a uniformly charged circular disc of radius 3 cm is 460V. What is the total charge on the disc? |
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Answer» SOLUTION :Data supplied, V=460 volts `r=3 xx 10^(-2)m` Potential (V) `=(sigma r)/(2epsi_(0))` `sigma =(2epsi_(0)V)/(r)" But ",sigma=(q)/(pir^(2))` `q/(pi r^(2))=(2epsi_(0)V)/(r)` `q= (2PI epsi_(0) Vr)` `=2 xx 3.14 xx 8.854 xx 10^(-12) xx 460 xx 3 xx 10^(-2)` =0.7673nC  Surface charge density of disc `sigma(("say"))` Consider a ring of radius x and thickness dx. Charge of this ring `=2pi xdx sigma` Potential at the centre due to this ring `=(1)/(4pi epsi_(0)) (2pi x sigma dx)/(x)=(sigma)/(2epsi_(0)) dx` Whole disc (potential) `=sigma/(2epsi_(0)) UNDERSET(0)overset(x)int dx=(sigma)/(2epsi_(0)) r` |
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