A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb

Question

A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value of Q is ______ nC. $(ε_{0} = 8.85 \times 10^{- 12} C^{2} {/Nm}^{2} and π = 3.14)$ [2026]

Smart Achievers · Accepted Answer

(1)

$E = \frac{2 k λ}{R} \sin (\frac{θ}{2}) = \frac{2 k λ}{R} \sin (\frac{180 °}{2}) = \frac{2 k λ}{R}$

$E = \frac{2 k λ}{R} = \frac{2 k Q}{π R^{2}} \Rightarrow Q = \frac{E π R^{2}}{2 k}$

$Q = \frac{100 \times 3.14 \times 35 \times 35 \times 10^{- 4}}{2 \times 9 \times 10^{9}} = 2.14 \times 10^{- 9} C$

Solution

Q.
A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value of Q is ______ nC. $(ε_{0} = 8.85 \times 10^{- 12} C^{2} {/Nm}^{2} and π = 3.14)$ [2026]

1 2.14

2 2.44

3 3.25

4 0.7

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