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A circular loop of wire with radius 2.00 cm and resistance 0.600 Ω is in a region of a spatially uniform magnetic field B⃗ that is perpendic
Question
A circular loop of wire with radius 2.00 cm and resistance 0.600 Ω is in a region of a spatially uniform magnetic field B⃗ that is perpendicular to the plane of the loop. At t = 0 the magnetic field has magnitude B0=3.00T. The magnetic field then decreases according to the equation B(t)=B0e−t/τ, where τ=0.500s.
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Physics
3 years
2021-08-20T00:37:18+00:00
2021-08-20T00:37:18+00:00 1 Answers
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Answer:
Incomplete questions
Let assume we are asked to find
Calculate the induced emf in the coil at any time, let say t=2
And induced current
Explanation:
Flux is given as
Φ=NAB
Where
N is number of turn, N=1
A=area=πr²
Since r=2cm=0.02
A=π(0.02)²=0.001257m²
B=magnetic field
B(t)=Bo•e−t/τ,
Where Bo=3T
τ=0.5s
B(t)=3e(−t/0.5)
B(t)=3exp(-2t)
Therefore
Φ=NAB
Φ=0.001257×3•exp(-2t)
Φ=0.00377exp(-2t)
Now,
Induce emf is given as
E= – dΦ/dt
E= – 0.00377×-2 exp(-2t)
E=0.00754exp(-2t)
At t=2
E=0.00754exp(-4)
E=0.000138V
E=0.138mV
b. Induce current
From ohms laws
V=iR
Given that R=0.6Ω
i=V/R
i=0.000138/0.6
i=0.00023A
i=0.23mA