Question

A 2 mC positive charge is located in vacuum at point P₁(3, -2, -4) and 5 μC negative charge is located at P₂ (1, -4, 2). What is the magnitude of force on the charge at P₁?
1. 2.04 N
2. 1.96 N
3. 2.91 N
4. 3.10 N

Answer 1

Correct Answer - Option 1 : 2.04 N

Diagram

The force between them is,

\(\left| F \right| = \frac{{\left| {{Q_1},\;{Q_2}} \right|}}{{4\pi \varepsilon {{\left| {{{\vec R}_{12}}} \right|}^2}}}\)

To find \(\left| {{R_{12}}} \right| = \sqrt {{{\left( {3 - 1} \right)}^2} + {{\left( { - 2 + 4} \right)}^2} + \left( { - 4 - 2} \right)} \)

\(\left| {{R_{12}}} \right| = \sqrt {44} \)

\(\Rightarrow \left| F \right| = \frac{{2\; \times\; {{10}^{ - 3}}\; \times \;5\; \times \;{{10}^{ - 6}}}}{{4\pi \; \times \;\frac{1}{{36\pi }}\; \times\; {{10}^{ - 9}}\; \times \;{{\left( {\sqrt {44} } \right)}^2}}}\)

\(\left| F \right| = \frac{{2\; \times \;5\; \times \;9}}{{44}}\)

\(F = \frac{{90}}{{44}} = 2.045\;N\)