Question 568: Electrostatics & Capacitance

Question

Four charges equal to -$$Q$$ are placed at the four corners of a square and  a charge $$q$$ is at its center. If the system is in equilibrium the value of $$q$$ is

Accepted Answer

Net field at A should be zero
$$\sqrt 2 \,{E_1} + {E_2} = {E_3}$$
$$	herefore$$ $${{kQ 	imes \sqrt 2 } \over {{a^2}}} + {{kQ} \over {\left( {\sqrt 2 a} ight)}} = {{kq} \over {{{\left( {{a \over {\sqrt 2 }}} ight)}^2}}}$$
$$ \Rightarrow {{Q\sqrt 2 } \over 1} + {Q \over 2} = 2q$$
$$ \Rightarrow q = {Q \over 4}\left( {2\sqrt 2  + 1} ight).$$

Answer

$$ - {Q \over 2}\left( {1 + 2\sqrt 2 } \right)$$

Answer

$${Q \over 4}\left( {1 + 2\sqrt 2 } \right)$$

Answer

$$ - {Q \over 4}\left( {1 + 2\sqrt 2 } \right)$$

Answer

$${Q \over 2}\left( {1 + 2\sqrt 2 } \right)$$

Electrostatics & Capacitance

Four charges equal to -$Q are placed at the four corners of a square and a charge q is at its center. If the system is in equilibrium the value of q$ is

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