A 12 μC charge is placed at the distance of 10 cm from a linear charge of 100 μC uniformly distributed once the length of 10 cm as shown in figure. Find the force on 12 μC charge.

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

Given,
linear charge ,

λ = 100 μC

and, a

12 μ C

charge is placed at a distance of 10 cm.

Therefore,

Force on 12 μC charge due to an elementary part of the linear charge,

dF = \frac{1}{4 {πε}_{0}} . \frac{(λdx) 12 \times 10^{- 6}}{x^{2}} = \frac{1}{4 π ε_{\circ}} \frac{q}{l} . 12 \times 10^{- 6} \frac{d x}{x^{2}} = 9 \times 10^{9} \times \frac{100 \times 10^{- 6}}{10 \times 10^{- 2}} \times 12 \times 10^{- 6} \times \frac{dx}{x^{2}} = 1.08 \frac{dx}{x^{2}}

Net force on 12 μC charge

F = \int dF = 1.08 \int_{0.10}^{0.20} \frac{dx}{x^{2}} = 1.08 {[- \frac{1}{x}]}_{0.01}^{0.20} = 1.08 [\frac{1}{0.10} - \frac{1}{0.20}] = 10.8 [1 - \frac{1}{2}] = 5.4 N .

For Daily Free Study Material Join wiredfaculty