**Answer the following question.**

When a conducting loop of resistance 10 Ω and area 10 cm^{2} is removed from an external magnetic field acting normally, the variation of induced current-I in the loop with time t is as shown in the figure.

Find the

(a) total charge passed through the loop.

(b) change in magnetic flux through the loop

(c) magnitude of the field applied

#### Solution

`I = ("dq")/("dt") ⇒ "dq = "I"d"t"`

Hence area under the I-t curve gives charge flown.

Area of the I-t curve (as given in the question) = `1/2 xx 2 xx 1/2 = 0.5`

Total charge passed through the loop = 0.5 C

Now we know

`Δ"Q" = (Δvarphi)/"R"`

`Δvarphi = Δ"Q" xx "R" = 1/2 xx 10Omega = 5 "Wb"`

Charge in magnetic flux through the loop= 5 Wb

`Δvarphi = "B" (Δ"A")`

`5 = "B" (0.001)`

`"B" = 5000 "T"`

The magnitude of the field applied = 5000 T