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Moving Charges And Magnetism

Question
CBSEENPH12037603
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Two circular coils made of similar wires but of radii 20 cm and 40 cm are connected in parallel.
What will be the ratio of the magnetic field at their centres?

Solution

Given, two circular coils mad of similar wires.
Radius of first wire, r1 = 20 cm
Radius of second wire, r2 = 40 cm
Magnetic field at the centre of circular coil of radius r, turns N, and current I passing in coil is 
 B = μ0NI2rB = μ0N2rVR                                       [R = resistance of coil]B = μ0N2rV2πrx                             [x is resistance per unit length]B = μ0NV4πxr2 

As coils are is parallel so potential difference ‘V’ are equal in both coils 

∴                V∝1r2
                  B1B2 = r22r12
                  B1B2 = 40202B1B2 = 4    B1:B2 = 4:1
 

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M1 and M2 have the following particulars:
R1 = 10 Ω   N1 = 30,
A1 = 3.6 x 10–3 m2,  B1 = 0.25 T
R2 = 14 Ω;  N2 = 42,
A2 = 1.8 x 10–3 m2, B2 = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M2 and M1.

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