Question 593: Electrostats & Capacitance

Question

Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and (0, –2). The work required to put a fifth charge Q at the origin of the coordinate system will be -

Accepted Answer

Potential at origin = $${{KQ} \over 2} + {{KQ} \over 2} + {{KQ} \over {\sqrt {20} }} + {{KQ} \over {\sqrt {20} }}$$
(Potential at  $$\infty $$ = 0)
= KQ$$\left( {1 + {1 \over {\sqrt 5 }}} ight)$$
$$ 	herefore $$  Work required to put a fifth charge Q
at origin is equal to $${{{Q^2}} \over {4\pi {\varepsilon _0}}}\left( {1 + {1 \over {\sqrt 5 }}} ight)$$

Answer

$${{{Q_2}} \over {4\pi {\varepsilon _0}}}$$

Answer

$${{{Q^2}} \over {2\sqrt 2 \pi {\varepsilon _0}}}$$

Answer

$${{{Q_2}} \over {4\pi {\varepsilon _0}}}\left( {1 + {1 \over {\sqrt 3 }}} \right)$$

Answer

$${{{Q_2}} \over {4\pi {\varepsilon _0}}}\left( {1 + {1 \over {\sqrt 5 }}} \right)$$

Electrostats & Capacitance

Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and (0, –2). The work required to put a fifth charge Q at the origin of the coordinate system will be -

Choose the correct answer: