If the shown system is in equilibrium, then the surface charge density on the large sheet is
[Take ϵ0=9×10−12C2/Nm2 and g=10m/s2]
A
7.8×10−7C/m2
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B
4.8×10−7C/m2
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C
6.8×10−7C/m2
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D
5.8×10−7C/m2
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Solution
The correct option is A7.8×10−7C/m2 Free body diagram of the system is given below:
From equilibrium of forces along x−axis, Tsin60∘=qE.....(1)
From equilibrium of forces along y−axis, 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