Name: Electric Field: Time Varying Magnetic Field
Uploaded: 2019-07-19
Duration: 8 min 32 s
Description: Did you know that the cause of the movement of charges in a stationary circular conducting coil placed in a time-varying magnetic field is due to an induced...

Question

A secondary coil of

300

turns is wound closely on the toroid above. If the current in the primary coil is increased from zero to

2.0 A

in

0.05 s,

obtain the induced emf in the second coil.

Accepted Answer

We are given that:-

Number of turns of secondary coil $N_{1} = 300 .$

Change in current $∆ i = i_{f} - i_{i}$

$i_{f} = 2 A, i_{i} = 0 A .$

Change in current $∆ t = 0.05 s .$

$e = - N_{1} (\frac{∆ i}{∆ t}) .$

Put the value of given data:-

$\Rightarrow e = - 300 (\frac{2 - 0}{0.05 s}) .$

$\Rightarrow e = - 1200$

Magnetic flux linked with the second coil,

$ϕ_{2} = B \times A \times N_{2} .$

Where $N_{2}$ is a total number of turns of the second coil.

$ϕ = i \times 1.6 \times 10^{- 3} \times 12 \times 10^{- 4} \times 300 = 5.76 \times 10^{- 4} \times i W b .$

Initial flux, $ϕ_{i} = 5.76 \times 10^{- 4} \times 0 = 0 .$

Final magnetic flux linked with the second coil,

$\Rightarrow ϕ_{f} = 5.76 \times 10^{- 4} \times$ final current

$\Rightarrow ϕ_{f} = 5.76 \times 10^{- 4} \times 2.0 = 1.152 \times 10^{- 3} W b .$

Time taken, $∆ t = 0.05 s,$

Now, $ε = \frac{d ϕ}{d t} = \frac{1.152 \times 10^{- 3} W b}{0.05 s}$

$ε = 0.0234 V$ .

Hence, the correct answer is $ε = 0.0234 V$ .

A secondary coil of $300$ turns is wound closely on the toroid above. If the current in the primary coil is increased from zero to $2.0 A$ in $0.05 s,$ obtain the induced emf in the second coil.

Important Questions on Electromagnetic Induction

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