First slide

Electric field

Question

A ring of charge with radius 0.5 m has 0.002 $π$ m gap. If the ring carries a charge of +1 C, the electric field at the centre is

Moderate

A

7.5 × 10⁷.NC^–1
B

7.2 × 10⁷.NC^–1
C

6.2 × 10⁷.NC^–1
D

6.5 × 10⁷.NC^–1

Solution

$\frac{Q}{2 πr} = \frac{dq}{dl} dq = \frac{Q}{2 πr} . dl = \frac{1}{2 π x 0.5} = \frac{0.02 π}{1} = \frac{2}{1000} E = \frac{1}{4 {πε}_{0}} \frac{dq}{r^{2}} \Rightarrow 9 x 10^{9} x \frac{2 x 10^{- 3}}{{(\frac{1}{2})}^{2}}$
E = 7.2 × 10⁷ N/C

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