What is the minimum frequency with which a 200-turn,flat coil of cross sectional area 380 cm² can be rotated in a uniform 32-mT magnetic field if the maximum value of the induced emf is to equal 7.9 V? A) 0.19 Hz B) 2.3 Hz C) 5.2 Hz D) 32 Hz E) 0.032 Hz

Question

Quizplus · Accepted Answer

The induced emf in a coil of N turns rotating at an angular frequency ω in a magnetic field B is given by:

ε = NωBAcos(ωt)

The maximum value of ε occurs when cos(ωt) = 1. Therefore:

εmax = NωB̅A

where B̅ is the maximum (uniform) value of the magnetic field.

We can rearrange this equation to solve for the minimum angular frequency:

ωmin = εmax / (NBA̅)

Plugging in the given values, we have:

N = 200
A = 380 cm² = 0.038 m²
B̅ = 32 mT = 0.032 T
εmax = 7.9 V

Therefore:

ωmin = (7.9 V) / (200 × 0.038 m² × 0.032 T)

ωmin ≈ 5.16 Hz

So the minimum frequency at which the coil can be rotated to achieve the desired maximum emf is about 5.2 Hz, which corresponds to choice C.

What Is the Minimum Frequency with Which a 200-Turn,flat Coil