Respuesta :
Explanation:
It is given that,
Area of nickel wire, [tex]A=7.4\ cm^2=7.4\times 10^{-4}\ m^2[/tex]
Resistance of the wire, R = 2.4 ohms
Initial value of magnetic field, [tex]B_1=0.5\ T[/tex]
Final magnetic field, [tex]B_2=3\ T[/tex]
Time, t = 1.12 s
Let I is the induced current in the loop of wire over this time. Te emf induced in the wire is given by Faraday's law as :
[tex]\epsilon=-\dfrac{d\phi}{dt}[/tex]
[tex]\epsilon=-\dfrac{d(BA)}{dt}[/tex]
[tex]\epsilon=-A\dfrac{d(B)}{dt}[/tex]
[tex]\epsilon=-A\dfrac{B_2-B_1}{t}[/tex]
[tex]\epsilon=-7.4\times 10^{-4}\times \dfrac{3-0.5}{1.12}[/tex]
[tex]\epsilon=1.65\times 10^{-3}\ V[/tex]
Induced current in the loop of wire is given by :
[tex]I=\dfrac{\epsilon}{R}[/tex]
[tex]I=\dfrac{1.65\times 10^{-3}}{2.4}[/tex]
[tex]I=6.87\times 10^{-4}\ A[/tex]
So, the induced current in the loop of wire over this time is [tex]6.87\times 10^{-4}\ A[/tex]. Hence, this is the required solution.
The induced current in the loop of the wire will be
[tex]I=6.87\times10^{4}\ A[/tex]
What will be the induced current in the loop of wire?
According to Faraday's law whenever the conducting material is exposed to the influence of magnetic field then the emf is generated and the current is induced in the conducting material.
We have following information from question:
Area of nickel wire, [tex]A=7.40\ cm^2[/tex]
Resistance of the wire, R = 2.4 ohms
Initial value of magnetic field, [tex]B_1=0.500\ T[/tex]
Final magnetic field, [tex]B_2=3\ T[/tex]
Time, t = 1.12 s
Let I is the induced current in the loop of wire over this time. The emf induced in the wire is given by Faraday's law as :
[tex]e=\dfrac{-d\phi}{dt}[/tex]
[tex]e=-d\dfrac{(BA)}{dt}[/tex]
[tex]e=-A\dfrac{(B)}{dt}[/tex]
[tex]e=-A\dfrac{(B_2-B_1)}{t}[/tex]
[tex]e=\dfrac{7.4\times10^{-4}\times(30-0.5)}{1.12}[/tex]
[tex]e=1.65\times10^{-3}\ V[/tex]
The current induced in the wire will be given as:
[tex]I=\dfrac{e}{R}[/tex]
[tex]I=\dfrac{1.65\times10^{-3}}{2.4}[/tex]
[tex]I=6.87\times 10^{-4}\ A[/tex]
Thus the induced current in the loop of the wire will be
[tex]I=6.87\times10^{4}\ A[/tex]
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