A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of −2 × 10−9C from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm).
Charge located at the origin, q = 8 mC= 8 × 10−3 C
Magnitude of a small charge, which is taken from a point P to point R to point Q, q1 = − 2 × 10−9 C
All the points are represented in the given figure.
Point P is at a distance, d1 = 3 cm, from the origin along z-axis.
Point Q is at a distance, d2 = 4 cm, from the origin along y-axis.
Potential at point P, `V_1=q/(4piin_0xxd_1)`
Potential at point Q,`V_2=q/(4piin_0xxd_2)`
Work done (W) by the electrostatic force is independent of the path.
`therefore W=q_1 [V_2-V_1]`
Where , `1/(4piin_0)=9xx10^9 Nm^2C6-2`
Therefore, work done during the process is 1.27 J.