A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of –2 x 10^–9 C 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).

Solution

Given,
Charge, q =8 mC=8 x 10^–3 C is located at origin and the small charge q₀ =–2 x 10^–9C is taken from point P (0,0,3 cm) to a point Q (0,4 cm,0) through point R (0,6 cm,9 cm) as shown in the figure below.
Initial separation between q₀ and q is r_p = 3 cm = 0.03 m
Final separation between q₀ and q is r_Q = 4 cm = 0.04 m

Work done in taking the charge q₀ from point P to Q does not dependent on the path followed and depends only upon r_p and r_Q i.e., initial and final positions.
$W = \frac{1}{4 {πε}_{0}} {qq}_{0} (\frac{1}{r_{Q}} - \frac{1}{r_{p}})$ $W = 9 \times 10^{9} \times 8 \times 10^{- 3} \times (- 2 \times 10^{- 9}) \times (\frac{1}{0.04} - \frac{1}{0.03}) = 1.2 J .$

Note: Point R is irrelevant to the answer.

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Electrostatic Potential And Capacitance

A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of –2 x 10^–9 C 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).

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Electrostatic Potential And Capacitance

A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of –2 x 10–9 C 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).

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A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of –2 x 10^–9 C 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).