Question

1. A charged particle \( q_{1} \) is at position \( (2,-1,3) \). The electrostatic force on another charged particle \( q_{2} \) at (f) 0,0 ) is : (1) \( \frac{q_{1} q_{2}}{56 \pi \epsilon_{0}}(2 \hat{i}-\hat{j}+3 \hat{k}) \) (2) \( \frac{q_{1} q_{2}}{56 \sqrt{14 \pi} \epsilon_{0}}(2 \hat{i}-\hat{j}+3 \hat{k}) \) (3) \( \frac{q_{1} q_{2}}{56 \pi \epsilon_{0}}(\hat{j}-2 \hat{i}-3 \hat{k}) \) (4) \( \frac{q_{1} q_{2}}{56 \sqrt{14} \pi \epsilon_{0}}(\hat{j}-2 \hat{i}-3 \hat{k}) \)

Answer 1

Correct option is (2) \(F = \frac {q_1 q_2}{56 \sqrt {14} \pi \varepsilon _0} (2 \hat {i}-\hat {j}+ 3\hat {k})\)

Position vector, \(\vec {d}\)

\(\vec {d} = (2-0) \hat {i} - (1-0)\hat {j} + (3-0) \hat {k} = 2\hat {i}- \hat {j} + 3\hat {k}\)

\(d^3 = [2 \hat {i}-\hat {j} + 3\hat {k}. (2\hat {i})-\hat {j}+3\hat {k}]^{\frac {3}{2}}\)

\(d^3 = 14\sqrt{14}\)

Electrostatic force F

\(F =\frac {1\,q_1q_2}{4\pi \varepsilon _0 \,d^3}\vec {d} = \frac {q_1 q_2 (2 \hat {i}-\hat {j}+3\hat {k})}{4\pi \varepsilon _0\,14\sqrt {14}}\)

\(F = \frac {q_1 q_2}{56 \sqrt {14} \pi \varepsilon _0} (2 \hat {i}-\hat {j}+ 3\hat {k})\)