Concept explainers
The circuit in Figure P3 1.61 is located in a magnetic field whose magnitude varies with lime according to the expression B = 1.00 × 10-3 t, where B is in teslas and f is in seconds. Assume the resistance per length of the wire is 0.100 Ω/m. Find the current in section PQ of length a = 65.0 cm.
The current in the section PQ.
Answer to Problem 31.61AP
The current in the section PQ is
Explanation of Solution
Given Info: The time varying magnetic field is
The circuit diagram is as shown below.
Figure (1)
For loop 1:
The resistance of the loop is,
Here,
The length of PQ is
The area of the loop is,
Thus, the area of the loop 1 is
The flux induced in the loop is,
Here,
The angle between the normal component of the area and the magnetic field is,
Substitute
The emf induced in the loop is,
Substitute
Thus, the induced emf in the loop 1 is
The current in the loop is
Apply Kirchhoff’s loop rule in loop 1.
Substitute
For loop (2):
The resistance of the loop is,
The area of the loop is,
Thus, the area of the loop 2 is
The flux induced in the loop is,
The angle between the normal component of the area and the magnetic field is,
Substitute
Thus, the flux induced in the loop is
The emf induced in the loop is,
Substitute
Thus, the induced emf in the loop 2 is
The current in the loop is
Apply Kirchhoff’s loop rule in loop 2.
Substitute
From the figure (1) the current in the arm PQ is,
Substitute
Rearrange the equation (2) for
Substitute
Substitute
Rearrange the above equation for
Substitute
Further solve the above equation.
The current in PQ is
Conclusion:
Therefore, the current in the PQ arm is
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Chapter 31 Solutions
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