Question

When a conducting loop of resistance 10 Ω and area 10 cm² is removed from an external magnetic field acting normally, the variation of induced current in the loop with time is shown in the figure.

Find the

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

Answer 1

Given: Area (A) = 10 cm² = `10/10000` m²

Resistance (R) = 10 Ω

From the graph, change in current = 0.4 A

Change in time = 1.0 s

i. Total charge passed through the loop = current × time

= 0.4 × 1.0

= 0.4 C

ii. |e| = `(Delta phi)/(Delta t)`

Or, iR = `(Delta phi)/(Delta t)`

Or, 0.4 × 10 = `(Delta phi)/1.0`

∴ Change in flux (ΔΦ) = 4 Wb

iii. |e| = `A (Delta B)/(Delta t)`

Or, iR = `A (Delta B)/(Delta t)`

Or, 0.4 × 10 = `10/10000 (Delta B)/1.0`

∴ ΔB = 4000 T