A coil formed by wrapping 80 turns of wire in the shape of asquare is positioned in a magnetic field so that the normal to the plane ofthe coil makes an angle of 60.0∘ with the direction of the field. When themagnetic field is increased uniformly from 100 mT to 500 mT in 0.20 s,the emf of magnitude 50.0 mV is induced in the coil. What is the totallength of the wire in the coil?

Question
Asked Oct 14, 2019
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A coil formed by wrapping 80 turns of wire in the shape of a
square is positioned in a magnetic field so that the normal to the plane of
the coil makes an angle of 60.0
∘ with the direction of the field. When the
magnetic field is increased uniformly from 100 mT to 500 mT in 0.20 s,
the emf of magnitude 50.0 mV is induced in the coil. What is the total
length of the wire in the coil?

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Expert Answer

Step 1

Given,

N 80
0=60°
e 50 mV
At = 0.2 sec
B 100 mT
В,
B2 500 mT
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N 80 0=60° e 50 mV At = 0.2 sec B 100 mT В, B2 500 mT

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Step 2

Emf in magnetic field is calculated as,

e N
ΔΜ
φ= Β.4-ΒA cos θ
, ΔΒΑ cos θ
e = N
Δt
eAt
A =
ΝΔBcos θ
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e N ΔΜ φ= Β.4-ΒA cos θ , ΔΒΑ cos θ e = N Δt eAt A = ΝΔBcos θ

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Step 3

By substituting the ...

едt
A =
NABCOS
(50x103)(0.2)
А-
80x(400x103)cos 60°
A 6.25 x 10 m2
Side of square,a = 0.025m
So,total length of wire = 80(4x 0.025) = 8m
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едt A = NABCOS (50x103)(0.2) А- 80x(400x103)cos 60° A 6.25 x 10 m2 Side of square,a = 0.025m So,total length of wire = 80(4x 0.025) = 8m

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Physics

Electromagnetic Induction

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