Question

A coil with an average diameter of 0.02 m is placed perpendicular to a magnetic field of 6000 t (tesla). If the induced emf is 11 v when the magnetic field is changed to 1000 t in 4 s, is the number of turns in the coil?

Answer 1

Answer: 28 turns

Explanation:

ℰ = -dФ/dt  ⇒ -N×A×dB/dt

ΔB=Bf - Bi = 1000-6000 ⇒ -5000 T

Δt=4 - 0 ⇒4secs

ℰ = -N × πd²/4 × (-5000)/4 ⇒N × π(0.02)²/4 × 5000/4 ⇒ N×0.3925

11V = N×0.3925⇒ N ≈ 28 turns

Answer 2

The number of turns in the coil is 28.

Explanation:

It is given that,

Diameter of the coil, d = 0.02 m

Radius, r = 0.01 m

Initial magnetic field, $B_i = 6000\ T$

Final magnetic field, $B_f = 1000\ T$

Induced emf, E = 11 V

Time, t = 4 s

The expression for the induced emf is given by :

$\epsilon=\dfrac{d\phi}{dt}$

$\phi$ = magnetic flux

$\epsilon=-N\dfrac{d(BA)}{dt}$

$\epsilon=-AN\dfrac{d(B)}{dt}$

$\epsilon=-AN\dfrac{B_f-B_i}{t}$

$11=N\pi (0.01)^2\times \dfrac{1000-6000}{4}$

N = 28

So, the number of turns in the coil is 28. Hence, this is the required solution.

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Induced emf

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