A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 . If the vertical component of earth’s magnetic field at that place is and electrical resistance of the coil is 12.56, then the maximum induced curr

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Solution

Q.
A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 $rad$ $s^{- 1}$ . If the vertical component of earth’s magnetic field at that place is $2 \times 10^{- 5} T$ and electrical resistance of the coil is 12.56 $Ω$ , then the maximum induced current in the coil will be [2022]

1 0.25 A

2 1.5 A

3 1 A

4 2 A

Ans.
(3)

Given, number of turns $(N) = 1000$

Radius $(r) = 10$ $m$

Angular velocity $(ω) = 2$ $rad$ $s^{- 1}$

Magnetic field $(B) = 2 \times 10^{- 5} T$

Electrical resistance $(R) = 12.56 Ω$

Maximum induced emf $= N ω A B$

Here area of the circular coil $A = π r^{2}$

$ε = N ω π r^{2} B = 1000 \times 2 \times 3.14 \times {(10)}^{2} \times 2 \times 10^{- 5}$

$ε = 12.56 V$

The maximum induced current is, $i_{max} = \frac{ε}{R}$

$\Rightarrow i_{max} = \frac{12.56}{12.56} = 1$ $A$

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