question_answer

Three point charges are placed on the following points along the X-axis: \[4\mu C\] at x = 0, \[3\mu C\] at x = 20 cm; and \[-5\mu C\] at x = 40 cm. What is the value of force on -3u€ (approximately):

A) 6N      

B) 4N     

C) 3N                              

D) 5N

Correct Answer: A

Solution :

[a] 6 N \[{{F}_{1}}=\left( \frac{1}{4\pi {{\varepsilon }_{0}}} \right)\frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}\] \[=\frac{9\times {{10}^{9}}\times 3\times {{10}^{-6}}\times 4\times {{10}^{-6}}}{{{\left( 20\times {{10}^{-2}} \right)}^{2}}}=\frac{108\times {{10}^{-3}}}{4\times {{10}^{-2}}}=2.7\,N\]\[{{F}_{2}}=\frac{9\times {{10}^{9}}\times 3\times {{10}^{-6}}\times 5\times {{10}^{-6}}}{{{\left( 20\times {{10}^{-2}} \right)}^{2}}}\] \[=\frac{105\times {{10}^{-3}}}{4\times {{10}^{-2}}}=3.375\,N\] \[{{F}_{net}}={{F}_{1}}+{{F}_{2}}\] \[=2.7+3.375=6.075\,N\cong 6N\]