Question

I need a very clear explanation! Thank you!

Examples 7. Find the potential due to a point charge. Use infinity as reference assuming zero potential there.

Answer 1

Work is done against the applying field Let the distance between + q and unit positive change (+ 1) is x the electrostatic force between q and unit positive charge (+ 1) is x the electrostatic force between q and + 1 is given as: - f = kq (+ 1)/x^2__(i) so small work done to displace change + 1 through dx dw = F. dx implies dw = F dx cos 180 degree implies dw = -F dx__(ii) from equation (i) and (ii) dw = -kg/x^2 dx so total work By integrate eq (iii) from infinity to r. implies w = -integral^r_infinity fq/x^2 dx implies v = -kq integral^r_infinity 1/x^2 . dx \r\n v = -kq integral^r_infinity x^-2 dx = -kq [x^-2 + 1/-2 + 1]^r_infinity v = kq [1/x]^r_infinity implies v = kq [1/r - 1/infinity] implies v = kq/r k = 1/4 pi epsilon_0 v = 1 q/4 pi epsilon_0 r in vector v = q/4pi epsilon_0 r r