Charges 4Q , q and Q and placed along x -axis at positions x = 0,x = l/2 and x = l , respectively. v

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1. Electric Charges and Fields

normal

Charges $4Q$, $q$ and $Q$ and placed along $x$-axis at positions $x = 0,x = l/2$ and $x = l$, respectively. Find the value of $q$ so that force on charge $Q$ is zero

A$Q$

B$Q / 2$

C$-Q / 2$

D$-Q$

Solution

(d) The total force on $Q$
$\frac{{Qq}}{{4\pi {\varepsilon _0}{{\left( {\frac{l}{2}} \right)}^2}}} + \frac{{4{Q^2}}}{{4\pi {\varepsilon _0}{l^2}}}\,\, = 0$
$\frac{{Qq}}{{4\pi {\varepsilon _0}{{\left( {\frac{l}{4}} \right)}^2}}} = – \frac{{4{Q^2}}}{{4\pi {\varepsilon _0}{l^2}}}\,\, \Rightarrow \,\,q = – Q.$

Standard 12

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Solution

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