Question

A circular loop of area 3sq. M and resistance 3ohmis lying in yz plane. The magnetic induction of the location of the loop varies time as B=(2t3-6t2)i+3tj. The magnitude of maximum current in the loop during intervals from t=0 and t=2sec.

Answer 1

Answer:

6A

Explanation:

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Answer 2

The maximum current in the loop is 6 A.

Explanation:

Given that,

Area = 3 m²

Resistance = 3 ohm

Magnetic field $B=(2t^3-6t^2)i+3t j$

We need to calculate the potential difference

Using formula of potential difference

$V=-\dfrac{d\phi}{dt}$

$V=-\dfrac{d}{dt}(B\cdot A)$

Put the value into the formula

$V=-\dfrac{d}{dt}((2t^3-6t^2)i+3tj)\cdot 3i$

$V=-\dfrac{d}{dt}(6t^3-18t^2)$

$V=-(18t^2-36t)$

$V=-18t^2+36t$

At t = 0 , V =0

At  t = 1.

Put the value of t

$V=18\times1+36\times1$

$V=18 V$

We need to calculate the maximum current in the loop

Using ohm's law

$V=IR$

$I=\dfrac{V}{R}$

Put the value into the formula

$I=\dfrac{18}{3}$

$I=6\ A$

Hence, The maximum current in the loop is 6 A.

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Topic : Magnetic field

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