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Question
Answer the following 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-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
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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
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