Two concentric coplanar semi-circular conductors form part of two current loops as shown in the figure. If their radii are 11 cm and 4 cm, calculate the magnetic induction at the centre.

Solution

Given, two concentric coplanar semi-circular conductors.
Radius of inner loop, r₁ = 4 cm
Radius of outer loop, r₂ = 11 cm
Current carried by the loops is 20 A and 40 A respectively.
Magnetic field due to circular loop at centre is given by,

B = \frac{μ_{0} I}{2 r}

Magnetic induction at centre due 4 qudadrant of wire is,

= \frac{1}{4} \frac{μ_{0}}{2} (\frac{40}{r_{1}} - \frac{40}{r_{2}}) - \frac{1}{4} \frac{μ_{0}}{2} (\frac{20}{r_{1}} - \frac{20}{r_{2}}) = \frac{4 π \times 10^{- 7}}{8} [20 (\frac{1}{r_{1}} - \frac{1}{r_{2}})] = \frac{4 π \times 10^{- 7}}{8} [20 (\frac{1}{4 \times 10^{- 2}} - \frac{1}{11 \times 10^{- 2}})] = 5 \times 10^{- 5} weber / m^{2} (inward)

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 M_1.

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Moving Charges And Magnetism

Two concentric coplanar semi-circular conductors form part of two current loops as shown in the figure. If their radii are 11 cm and 4 cm, calculate the magnetic induction at the centre.

Some More Questions From Moving Charges And Magnetism Chapter

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