A flexible, circular conducting loop of radius 0.15 m and resistance 4.0 $\varOmega$ lies in a uniform magnetic field of 0.25 T. The loop is pulled on opposite sides by equal forces and stretched until its enclosed area is essentially zero m 2 , as suggested in the drawings. It takes 0.30 s to close the loop. -At what rate is heat generated in the loop? A)3.6 × 10^-³ W B)8.7 × 10^-⁴ W C)8.7 × 10⁴ W D)8.1 × 10⁵ W E)8.1 × 10^-⁵ W

Question

Quizplus · Accepted Answer

The rate of heat generated in the loop can be calculated using the formula: 
Power = I²R 
where I is the current flowing through the loop and R is its resistance.

The time taken to close the loop is 0.30 s, so the rate of change of area of the loop is:
dA/dt = (final area - initial area) / time taken
dA/dt = (0 - π(0.15)²) / 0.30
dA/dt = -0.2356 m²/s

The emf induced in the loop due to the change in the magnetic flux is given by:
emf = -dΦ/dt
where Φ is the magnetic flux through the loop. Since the loop is circular and the field is uniform, the magnetic flux is given by:
Φ = BA
where B is the magnetic field strength and A is the area of the loop.

Thus, emf = -B(dA/dt) = 0.25 x 0.2356 = 0.059 V

The current flowing through the loop is given by:
I = emf/R = 0.059 / 4.0 = 0.0148 A

Finally, the rate of heat generated in the loop is:
Power = I²R = (0.0148)² x 4.0 = 0.0008264 W = 8.7 x 10⁻⁴ W, which is closest to option B.

A Flexible, Circular Conducting Loop of Radius 0 Ω\varOmegaΩ Lies in a Uniform Magnetic Field of 0

A Flexible, Circular Conducting Loop of Radius 0 $\varOmega$ Lies in a Uniform Magnetic Field of 0