Question

Two equal unlike charges, placed 3 cm. Apart in air. attract each other with a force of 40 N. The magnitude of each charge in micro coulombs is, take $ \frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}}\,SI $ units:

• A. 0.2
• B. 2
• C. 20
• D. 200

Answer 1

Answer: (B)

Force of attraction between two point charges $ {{q}_{1}} $ and $ {{q}_{2}} $ at separation r is given by $ F=\frac{1}{4\pi {{\varepsilon }_{0}}}\times \frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}} $ (Here: $ r=3cm=3\times {{10}^{-2}}m, $ $ F=40N,\frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}} $ ) $ 40=\frac{9\times {{10}^{9}}\times q\times q}{9\times {{10}^{-4}}} $ $ {{q}^{2}}=\frac{9\times 40\times {{10}^{-4}}}{9\times {{10}^{9}}} $ $ {{q}^{2}}=40\times {{40}^{-13}}=4\times {{10}^{-12}} $ = $ q=2\times {{10}^{-6}}=2\mu C $