A constant uniform magnetic field of 0.50 T is applied at right angles to the plane of a flat rectangular loop of area 3.0 × $10^{ - 3}$ $m ^ { 2 }$ If the area of this loop changes steadily from its original value to a new value of 1.6 × 10^-3 m² in 1.6 s,what is the emf induced in the loop? A)1.6 × $10 ^{- 2}$ V B)0 V C)7.5 × $10^{ - 2}$ V D)4.4 × $10^{ - 4}$ V E)9.0 × $10 ^{- 2}$ V

Question

Quizplus · Accepted Answer

The emf induced in a loop is given by the formula:
emf = -Δφ/Δt

where Δφ is the change in magnetic flux linked with the loop, and Δt is the time interval during which the change occurs.

In this case, the loop is initially perpendicular to the magnetic field, so the magnetic flux linked with the loop is:

φ1 = B*A = 0.50 * 3.0 × 10^-3 = 1.5 × 10^-3 Tm^2

When the area of the loop changes to a new value of 1.6 × 10^-3 m^2, the magnetic flux linked with the loop becomes:

φ2 = B*A = 0.50 * 1.6 × 10^-3 = 8.0 × 10^-4 Tm^2

The change in magnetic flux is thus:

Δφ = φ2 - φ1 = (8.0 - 1.5) × 10^-4 Tm^2 = 6.5 × 10^-4 Tm^2

The time interval during which the change occurs is given as 1.6 seconds. Therefore, the emf induced in the loop is:

emf = -Δφ/Δt = -(6.5 × 10^-4)/1.6 = -4.4 × 10^-4 V

The negative sign indicates the direction of the emf, according to Lenz's law.

A Constant Uniform Magnetic Field of 0 10−310^{ - 3}10−3 m2m ^ { 2 }m2

A Constant Uniform Magnetic Field of 0 $10^{ - 3}$ $m ^ { 2 }$