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Question

The electric field between two parallel square metal plates is $$130 N/C$$. The plates are $$0. 85 m$$ on a side and are separated by $$3.0 cm$$. What is the charge on each plate (assume equal and opposite)' Neglect edge effects

A
$$8.3 \times 10^{-10} C$$
B
$$5.6 \times 10^{-10} C$$
C
$$7.6 \times 10^{-12} C$$
D
$$4.1 \times 10^{-12} C$$
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Solution
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Correct option is A. $$8.3 \times 10^{-10} C$$
The electric field between two close parallel plates is,
$$E=\dfrac{\sigma}{\epsilon_0}$$
surface charge density is
$$\sigma = Q/A$$
$$E=\dfrac{\dfrac{Q}{A}}{\epsilon_0}$$$$=\dfrac{Q}{\epsilon_0A}$$
$$Q=\epsilon_0EA$$
$$=\epsilon_0El^2$$
$$Q=(8.85\times 10^{-12}C^2N.m^2)(130N/C)(0.85m)^2$$
$$=8.3\times 10^{-10}C$$

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