A point charge +q moves from point P to origin O along the path PQRO in a uniform electric field E . Find the work done by the field

Question

A point charge +q moves from point P to origin O along the path PQRO in a uniform electric field E . Find the work done by the field (A)  - 2qEa  (B)  2qEa  (C)  8qEa  (D)  - 4qEa

Tardigrade Admin · Accepted Answer

As the electrostatic force are conservative, work done is independent of path. Effective displacement
in going from

P

to

D

along any path

= PO

= (0 - 2 a) \hat{i} + (0 - b) \hat{j} + (0 - 0) \hat{k} = - 2 a \hat{i} - b \hat{j}

Force on charge,

F = (qE) \hat{i}

Now, work done

= F \cdot PO = (qE \hat{i}) \cdot (- 2 a \hat{i} - b \hat{j})

= - 2 qE a

Q. A point charge $+ q$ moves from point $P$ to origin $O$ along the path $PQRO$ in a uniform electric field $E$ . Find the work done by the field

$- 2 qE a$

$2 qE a$

$8 qE a$

$- 4 qE a$

Q. A point charge +q moves from point P to origin O along the path PQRO in a uniform electric field E . Find the work done by the field

−2qEa

2qEa

8qEa

−4qEa

As the electrostatic force are conservative, work done is independent of path. Effective displacement in going from P to D along any path =PO =(0−2a)i^+(0−b)j^​+(0−0)k^=−2ai^−bj^​ Force on charge, F=(qE)i^ Now, work done =F⋅PO=(qEi^)⋅(−2ai^−bj^​) =−2qEa

Q. A point charge $+ q$ moves from point $P$ to origin $O$ along the path $PQRO$ in a uniform electric field $E$ . Find the work done by the field

$- 2 qE a$

$2 qE a$

$8 qE a$

$- 4 qE a$