Question

A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of `-2xx10^(-9)` from a point P(0, 0, 3cm) to a point Q (0, 4cm, 0) via a point R(0, 6cm, 9cm).

Answer 1

charge located at the origin , q=8 mc =`8xx10^(-3)C`
Magnitude of a small charge, which is taken from a point p to point R to point Q,`q_(1)=-2xx10^(-9)C`
All the points are represented in the given figure,

point P ios at a distance `d_(1)=3 cm `, fromt he origin along z-axis
point Q is at a distance , `d_(2)=4 cm, ` from the origin along y-axis .
potential at point p , `V_(1)=q/(4pi in_(0)xxd_(1))`
Potential at point Q, `V_(2)=q/(4pi in_(0)d_(2))`
work done (W) by the electrostatic force is independent of the path.
`:. W=q_(1) [V_(2)-V_(1)]`
`=q_(1)[q/(4pi in_(0)d_(2))-q/(4pi in_(0)d_(1)]`
`=(qq_(1))/(4pi in_(0))[1/(d_(2))-1/(d_(1))]....(i)`
Where, `1/(4pi in_(0))=9xx10^(9) Nm^(2)C^(-2)`
`:. W=9xx10^(9) xx8xx10^(-3)xx(-2xx10^(-9))[1/0.04-1/0.03]`
`=-144xx10^(-3)xx((-25)/3)`
=1.27 J
Therefore, work done during the process is 1.27 J.