Consider the situation of the previous problem. A charge of `2.0xx 10 ^(-4) C` is moved from the point A to the point B. find the change in electrical potential energy `U_B-U_A` for the cases (a) , (b) and ( c ).

Explanation

(a) the electric field is along x direction Thus potential difference between `(0,0) and (4,2) is, `
` dV=-edx=-20xx4 `
` =-80volt `
` Potential energy (U_B-U_A) between the points=dVxxq `
` =-80xx-2.0xx10^-4 `
` =160xx10^-4=0.016J `
` (b) A=(4m,2m),B=(6m,5m) `
` dV=-exxdx=-20xx2=-40v `
` Potential energy (U_B-U_A) between the points=dVxxq `
` =-40xx(-2xx10^-4) `
` 80xx10^-4=0.008J `
` (c) A=(0,0) B=(6m,5m) `
` dV=-E.dx=-20xx6 `
` -120V `
` potential energy (U_B-U_A) between the points A and B=dVxxq `
` =-120xx(-2xx10^-4) `
` 240xx10^-4=0.024J `