Physics

Problem

A coil has 100 turns, each of area

0.05 \text{ m}^2

and total resistance

1.5 \Omega

. It is inserted at an instant in a magnetic field of

90 \text{ mT}

, with its axis parallel to the field. The charge induced in the coil at that instant is : (A)

3.0 \text{ mC}

(B)

0.30 \text{ C}

(C)

0.45 \text{ C}

(D)

1.5 \text{ C}

Intuitive explanation

The key here is electromagnetic induction and the relationship between charge and flux change. When the coil is inserted into the field, the magnetic flux through it changes dramatically—from zero to its maximum value. Rather than worrying about the time it takes, use Faraday's law in its integral form: the total charge induced depends only on the total change in flux and the resistance, not on how fast the change happens. Calculate the flux change ( $\Delta \Phi = NBA$ ), then find the charge using $Q = \Delta \Phi / R$ .

Intuitive explanation

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