A point charge q moves from point P to pont S along the path PQRS (fig.) in a uniform electric field E pointing parallel to the poistive direction of the X-axis. The coordinates of the points P, Q, R and S are(a, b, O), (2a, O, O)(a, -b,`ulO`) and `(O, O, O) respectively. The work done by the field in the above process is given by the expresison............

Answer

`-q E a`

Explanation

Here, `P(a,b,0), Q(2a,0,0), R(a, -b, 0) and S(0,0,0)`, fig

Effective desplacement is going from P to S via any path is
`= vec(PS) = (0-a) hat(i) + (0-b) hat(j) + (0-0) hat(k)`
`= -a hat(i) - b hat(j)`
force on the charge . `vec(F) = qE hat(i)`
work done, `W = vec(F). vec(PS)`
`= q E hat(i). (-a hat(i) - b hat(j))`
`= -q E a`
Negative sign shows that work is done against the electric field by some exteranal agency moving the charge.