In: Physics
Consider a small length "dl" of the complete loop having small charge "dq"
Q = total charge on the loop
R = radius of the loop
L = length of the loop = circumference = 2R
small charge on the small length is given as
dq = (Q/(L)) dl
dq = (Q/(2R)) dl
Small electric potential at the center due to small length is given as
dV = k dq/R
dV = k (Q/(2R)) dl/R
Total electric potential is given as
V = k (Q/(2R)) /R dl
V = k (Q/(2R)) (2R /R )
V = kQ/R
Since the direction of motion of the charge is perpendicular to the electric field, and we know that along the perpendicular direction of electric field, electric potential does not change., hence change in potential energy of the charge is zero.