Question

A circular conducting loop of radius 23.0 cm is located in a region of homogeneous magnetic field of magnitude 0.500 T pointing perpendicular to the plane of the loop. The loop is connected in series with a resistor of 265 Ω. The magnetic field is now increased at a constant rate by a factor of 2.50 in 23.0s. Calculate the magnitude of the induced emf in the loop while the magnetic field is increasing.

Answer 1

Answer:

The magnitude of the induced emf is

Ф = 5.419 x 10⁻³ V

Explanation:

Given:

r = 23.0 cm = 0.23 m

β₁ = 0.50 T

β₂ = 2.50 * 0.50 T = 1.25 T

Calculate the magnitude of the induced emf the magnetic field is increasing

Ф = A * Δβ / Δt

A = π * r² = π * 0.23² m = 0.166 m²

Ф = 0.166m² * (1.25 - 0.5) T / 23 s

Ф = 5.419 x 10⁻³ V