First slide

Finding field strength using Gauss's Law

Question

l g of cork with a charge 1 μC floats motionless 1 cm above a large uniformly charged plane near the surface of the earth. The surface charge density of the plane, assuming it to be an infinite sheet, is

Moderate

A

$8.7 \times 10^{- 8} C / m^{2}$
B

$17.3 \times 10^{- 8} C / m^{2}$
C

Zero
D

$- 1 μC / m^{2}$

Solution

The cork floats motionless if the weight of the cork is equal to electrostatic force due to uniformly charged plane near the earth's surface, i.e.,
$mg = F_{e} = QE$
Now, electric field E due to large plane is
$E = \frac{σ}{2 ε_{0}} mg = \frac{σ}{2 ε_{0}} Q σ = \frac{2 ε_{0} mg}{Q} = \frac{2 \times 8.85 \times 10^{- 12} \times 10^{- 3} \times 9.8}{1 \times 10^{- 6}} = 17.3 \times 10^{- 8} C / m^{2}$

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