Calculating the induced emf in the coil.

문제)

A 30-turn circular coil of radius 4.00cm and resistance 1.00Ω is placed in a magnetic field directed perpendicular to the plane of the coil.

 

The magnitude of the magnetic field is B = 0.0100t + 0.0400t^2 (T)

 

Calculating the induced emf in the coil at t = 5.00s

 

풀이)

induced emf ε = -N × dΦ / dt임을 이용한다.

 

N = 30

radius of coil = 4.00cm = 4.00 × 10^-2 m

resistance of coil = 1.00 Ω

magnetic field B = 0.0100t + 0.0400t^2 (T)

time t = 5.00 s

Area (A) = (4.00 × 10^-2 m) × (4.00 × 10^-2 m) × π = 0.0016π m^2

 

Φ = ∫ B dA

dΦ / dt = A × dB / dt = A × (0.0100 + 0.0800t) = (0.0016π m^2) × (0.0100 + 0.0800t)

 

At t = 5.00 s

dΦ / dt = A × dB / dt = (0.0016π m^2) × (0.0100 + 0.0800 × 5.00) = 2.06 × 10^-3

 

ε = -N × dΦ / dt = -30 × 2.06 × 10^-3 = -61.8 × 10^-3 V

 

그러나 magnetic field의 direction이 perpendicular to the plane of the coil이므로, -를 곱해서 

답은 61.8 × 10^-3 V이다.