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Question

If the shown system is in equilibrium, then the surface charge density on the large sheet is
[Take ϵ0=9×1012 C2/Nm2 and g=10 m/s2]


A
7.8×107 C/m2
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B
4.8×107 C/m2
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C
6.8×107 C/m2
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D
5.8×107 C/m2
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Solution

The correct option is A 7.8×107 C/m2
Free body diagram of the system is given below:


From equilibrium of forces along xaxis,
Tsin60=qE.....(1)
From equilibrium of forces along yaxis,
Tcos60=mg.....(2)
From equation (1) and (2),
tan60=qEmg.....(3)

Electric field due to a plate having surface charge density σ is
E=σ2ϵ0

Substituting this in (3), we get
tan60=qσ2ϵ0mg

σ=2ϵ0mgtan60q

σ=2×9×1012×10×103×10×tan604×106

σ=7.8×107 C/m2

Hence, option (d) is the correct answer.

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