Question

A conducting rectangular loop of area 5 cm² and resistance 4 Ω is removed from a region of uniform magnetic field, acting normal to the plane of the loop. The value of induced current I in the loop varies with time t, as shown in the figure.

Find:

1. total charge that passed through the loop
2. change in magnetic flux through the loop
3. magnitude of magnetic field in the region

Answer 1

The charge flowing through a loop is equal to the area under the current-time graph. The change in flux is related to the charge and resistance.

a. From the graph, the I-t curve is a triangle with height I₀ = 0.3 A and base t = 0.6 s.

q = `1/2 xx "base" xx "height"`

= `1/2 xx 0.6 xx 0.3`

= 0.09 C

b. The relationship between charge and flux is:

q = `(Delta phi)/R`

∆Φ = q × R

= 0.09 × 4

= 0.36 Wb

c. The loop is removed from the field, so:

∆Φ = `phi_"initial" - phi_"final"`

= B × A − 0

= 5 × 10⁻⁴ m²    ...[Area A = 5 cm²]

B = `(Delta phi)/A`

= `0.36/(5 xx 10^-4)`

= `3600/5`

= 720 T