Question

If a coil of 40 turns and area 4.0 cm² is suddenly removed from a magnetic field, it is observed that a charge of 2.0×10⁻⁴ C flows into the coil. If the resistance of the coil is 80Ω, the magnetic flux density in Wb /m² is(a) 0.5(b) 1.0(c) 1.5(d) 2.0

Answer 1

answer : option (b)

explanation : we know, $Q_{in}=\frac{\Delta\phi}{R}$

where $\Delta\phi$ denotes change in magnetic flux. but we know, magnetic flux is the product of magnetic field and cross sectional area. e.g., $\phi=BA$

so, $Q_{in}=\frac{NBA}{R}$

where N is number of turns .

so, $B=\frac{Q_{in}R}{NA}$

here, $Q_{in}=2\times10^{-4}C$

resistance, R = 80Ω

cross sectional area , A = 4cm² = 4 × 10^-4 m²

number of turns , N = 40

so, B = (2 × 10^-4 × 80)/(40 × 4 × 10^-4)

hence, B = 1 Wb/m²

hence, option (b) is correct.