Question

A plane loop is shaped in the form as shown in figure with radii a = 20 cm and b = 10 cm and is placed in a uniform time varying magnetic field B = B₀ sin ωt, where B₀ = 10 mT and ω = 100 rad/s. The amplitude of the current induced in the loop if its resistance per unit length is equal to 50 × 10^-3 Ω/m. The inductance of the loop is negligible is ______ A.

Options

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Answer 1

A plane loop is shaped in the form as shown in figure with radii a = 20 cm and b = 10 cm and is placed in a uniform time varying magnetic field B = B₀ sin ωt, where B₀ = 10 mT and ω = 100 rad/s. The amplitude of the current induced in the loop if its resistance per unit length is equal to 50 × 10^-3 Ω/m. The inductance of the loop is negligible is 1 A.

Explanation:

Instantaneous flux

= πa² B cos 0° + πb² B cos 180°

= π (a² - b²) B

Φ = π (a² - b²) B₀ sin ωt 

e = `("d"phi)/"dt"`

i = `"e"/"R"`

i = `(pi("a"^2-"b"^2)"B"_0omegacosomega"t")/"R"`

i = ρ × 2π (a + b)

∴ i_max = `1/(2ℓ)("a"-"b")"B"_0omega`

= 1 Amp.