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Question
Answer the following question.
The magnitude of the electric field (in NC – 1) in a region varies with the distance r(in m) as
E = 10r + 5
By how much does the electric potential increase in moving from point at r = 11 m to a point at r = 10 m.
Solution
point A be given at r = 1 m, point B be given at r = 10 m
VA = potential at A
VB = potential at B
The relation between the electric field and potential difference is given by the relation,
`V_B - V_A = -int_A^B vec"E". d vec"r"`
`V_B-V_A = - int_1^10 (10r+5).dr`
= `-[(10r^2)/2 + 5r]_1^10`
= `-[((10(10)^2)/2 + 5xx 10) - ((10(1)^2)/2 + 5xx1)]`
= `-[550-10]`
= -540 V
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