Answer:
Current, I = 0.153 A
Explanation:
Given that,
Radius of the circular conducting loop, r = 0.5 m
Resistance of the resistor, [tex]R=10\ \Omega[/tex]
Magnetic field, B = 1 T
Angle with z axis, [tex]\theta=30^{\circ}[/tex]
Magnetic field increases to 10 T in 4 seconds
To find,
Magnitude of current.
Solve,
According to Faraday's law, the induced emf is given by:
[tex]\epsilon=\dfrac{\phi_f-\phi_i}{t}[/tex]
[tex]\phi_f\ and\ \phi_i[/tex] are final flux and the initial flux respectively.
[tex]\epsilon=NA\ cos\theta\dfrac{B_f-B_i}{t}[/tex]
[tex]\epsilon=1\times \pi (0.5)^2\ cos(30)\dfrac{10-1}{4}[/tex]
[tex]\epsilon=1.53\ V[/tex]
The magnitude of current can be calculated using the Ohm's law as :
[tex]I=\dfrac{\epsilon}{R}[/tex]
[tex]I=\dfrac{1.53}{10}[/tex]
I = 0.153 A
Therefore, the magnitude of the current that will be caused to flow in the loop is 0.153 A.
