Question

A closely wound search coil has an area of 3.12 cm2cm2 , 135 turns, and a resistance of 58.8 ΩΩ . It is connected to a charge-measuring instrument whose resistance is 43.4 ΩΩ . When the coil is rotated quickly from a position parallel to a uniform magnetic field to one perpendicular to the field, the instrument indicates a charge of 3.46×10−5 CC

Answer 1

B = 0.08395 T = 83.95 mT

Step-by-step explanation:

According to the Faraday's law of electromagnetic induction, the induced emf is given as

E = -N (dΦ/dt)

The minus sign indicates that the emf is induced in a direction opposite to the changing magnetic flux.

Magnitude of emf is

E = N (dΦ/dt)

From Ohm's law

E = IR

But I = (dQ/dt)

E = R (dQ/dt)

N (dΦ/dt) = R (dQ/dt)

N dΦ = R dQ

Integrating both sides,

NΦ = RQ

But, Φ = BA

N BA = RQ

B = (RQ/NA)

R = 58.8 + 43.4 = 102.2 Ω

Q = (3.46×10⁻⁵) C

A = 3.12 cm² = (3.12 × 10⁻⁴) m²

N = 135

B = (102.2 × 3.46×10⁻⁵)/(135 × 3.12 × 10⁻⁴)

B = 0.0839534663 T = 0.08395 T = 83.95 mT

Hope this Helps!!!