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.

Answer 1

point A be given at r = 1 m, point B be given at r = 10 m

V_A = potential at A 

V_B = 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`

= `- 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