A flat circular coil consisting of 50 turns and enclosing an area of 0.02\text{ m}^2 is pl… — JAMB UTME

A flat circular coil consisting of $50$ turns and enclosing an area of $0.02\text{ m}^2$ is placed in a uniform magnetic field directed vertically upwards. The magnitude of the magnetic field decreases steadily from $0.5\text{ T}$ to $0.1\text{ T}$ in a time interval of $0.2\text{ s}$ . If the total electrical resistance of the coil is $5.0\text{ }\Omega$ , what is the magnitude and direction of the induced current in the coil when viewed from above?

$0.4\text{ A}$ in an anticlockwise directionCevap
B
$0.4\text{ A}$ in a clockwise direction
C
$1.0\text{ A}$ in an anticlockwise direction
D
$1.0\text{ A}$ in a clockwise direction

Cevap

0.4\text{ A}

in an anticlockwise direction

According to Faraday's law, the induced e.m.f. is given by

E = N A \frac{\Delta B}{\Delta t} = 50 \times 0.02 \times \frac{0.4}{0.2} = 2.0\text{ V}

. By Ohm's law, the current magnitude is

I = \frac{2.0\text{ V}}{5.0\text{ }\Omega} = 0.4\text{ A}

. By Lenz's law, because the upward magnetic field is decreasing, the coil opposes this decrease by generating an upward magnetic field. By the right-hand grip rule, an upward magnetic field corresponds to an anticlockwise current flow when viewed from above.

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Calculate the magnitude of the rate of change of magnetic field strength

\frac{\Delta B}{\Delta t} = \frac{0.5\text{ T} - 0.1\text{ T}}{0.2\text{ s}} = \frac{0.4\text{ T}}{0.2\text{ s}} = 2.0\text{ T/s}

Faraday's law depends on the rate at which the magnetic flux changes over time.

Calculate the magnitude of the induced electromotive force (e.m.f.)

E = N A \left(\frac{\Delta B}{\Delta t}\right) = 50 \times 0.02\text{ m}^2 \times 2.0\text{ T/s} = 2.0\text{ V}

The total induced e.m.f. is proportional to the number of turns and the enclosed area.

Determine the magnitude of the induced current using Ohm's law

I = \frac{E}{R} = \frac{2.0\text{ V}}{5.0\text{ }\Omega} = 0.4\text{ A}

Current equals induced voltage divided by total coil resistance.

Determine the direction of the induced current using Lenz's law and the right-hand rule

Anticlockwise direction when viewed from above

The upward magnetic field is decreasing, so the induced current must produce its own upward magnetic field to oppose the reduction in magnetic flux.

Anahtar Kavram

Faraday's Law and Lenz's Law of Electromagnetic Induction

Tahmini Süre:2m 0s

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