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Question
The magnitude of the electric field (in NC – 1) in a region varies with the distance r(in m) as
E = 10 r + 5
By how much does the electric potential increase in moving from point at r = 1 m to a point at r = 10 m.
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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,
VB − VA = `-int_A^B vec E * d vec r`
= `- int_1^10 (10 r + 5) * dr`
= `-[(10 r^2)/2 + 5 r]_1^10`
= `-[((10(10)^2)/2 + 5 xx 10) - ((10(1)^2)/2 + 5 xx 1)]`
= `-[550 - 10]`
= −540 V
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