(a) Using Biot-Savart law to derive an expression for the magnetic flux density $B$ at the centre of a circular loop of wire of radius $a$ , if the loop carries a steady current $I$ . (10 marks) (b) A uniformly charged circular ring of radius $R$ carries a total charge $Q$ and is rotating about its axis at a constant angular velocity $ω rad / s$ . Calculate the magnetic field strength at the centre of the circular ring. (5 marks) $[\frac{ω Q}{4 π R} A / m] (Hint: I = \frac{Q}{t} = \frac{Q}{2 π / ω} = \frac{ω Q}{2 π})$

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(a) Using Biot-Savart law to derive an expression for the magnetic flux density

B

at the centre of a circular loop of wire of radius

a

, if the loop carries a steady current

I

. (10 marks) (b) A uniformly charged circular ring of radius

R

carries a total charge

Q

and is rotating about its axis at a constant angular velocity

ω rad / s

. Calculate the magnetic field strength at the centre of the circular ring. (5 marks)

[\frac{ω Q}{4 π R} A / m] (Hint: I = \frac{Q}{t} = \frac{Q}{2 π / ω} = \frac{ω Q}{2 π})

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