Question

# Consider the configuration of a system of four charges each of value $$+ q.$$ Find the work done by external agent in changing the configuration of the system from figure (a) to figure (b).

Solution

## $${U_1} = K{q^2}\left\{ {\dfrac{1}{a} + \dfrac{1}{{\sqrt 2 a}} + \dfrac{1}{a} + \dfrac{1}{a} + \dfrac{1}{{\sqrt 2 a}} + \dfrac{1}{a}} \right\}$$$$= K{q^2}\left\{ {\dfrac{4}{a} + \dfrac{2}{{\sqrt 2 a}}} \right\}$$$${U_2} = K{q^2}\left\{ {\dfrac{1}{{\sqrt 2 a}} + \dfrac{1}{{2a}} + \dfrac{1}{{\sqrt 2 a}} + \dfrac{1}{{\sqrt 2 a}} + \dfrac{1}{{2a}} + \dfrac{1}{{\sqrt 2 a}}} \right\}$$$${U_2} = K{q^2}\left\{ {\dfrac{2}{{2a}} + \dfrac{4}{{\sqrt 2 a}}} \right\}$$$$W = - \left\{ {{U_1} - {U_2}} \right\} = - K{q^2}\left\{ {\dfrac{{4 + \sqrt 2 }}{a}} \right\} - K{q^2}\left\{ {\dfrac{{1 + 2\sqrt 2 }}{a}} \right\}$$$$W = - K{q^2}\left\{ {\dfrac{{4 + \sqrt 2 - 1 - 2\sqrt 2 }}{a}} \right\}$$$$\boxed{W = - K{q^2}\left\{ {\dfrac{{3 - \sqrt 2 }}{a}} \right\}}$$Physics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More