(a)
The area bounded by the rectangular coil.
(a)
Answer to Problem 3SP
The area bounded by the rectangular coil is
Explanation of Solution
Given info: The length of rectangular coil is
The coil provided is rectangular in shape. Therefore area of coil is found by multiplying the breadth and length.
Write the equation to find the area of a rectangular loop.
Here,
Substitute
Conclusion:
Therefore, the area of the rectangular coil is
(b)
The maximum value of magnetic flux passing through the rectangular coil as it is turned.
(b)
Answer to Problem 3SP
The maximum value of magnetic flux that is passing through the rectangular coil is
Explanation of Solution
Given info: Magnetic field applied is
Write the equation to find the magnetic flux passing through an area.
Here,
Maximum value of magnetic flux passes through the coil when the magnetic field and the rectangular coil are parallel to each other. Therefore the angle between rectangular coil and magnetic field
Substitute
Conclusion:
Therefore, the maximum value of magnetic flux that passes through the rectangular coil is
(c)
The minimum value of flux that passes through the rectangular coil as it is rotated.
(c)
Answer to Problem 3SP
The minimum value of magnetic flux that passes through the rectangular coil is zero.
Explanation of Solution
Given info: Magnetic field applied is
Write the equation to find the magnetic flux passing through an area.
Here,
Minimum value of magnetic flux passes through the coil when the magnetic field and the rectangular coil are perpendicular to each other. Therefore the angle between rectangular coil and magnetic field
Substitute
Conclusion:
Therefore, the minimum value of magnetic flux that passes through the rectangular coil is zero.
(d)
The time taken to change the flux from a maximum to minimum in a complete cycle.
(d)
Answer to Problem 3SP
The time taken for a change from maximum flux to minimum flux is
Explanation of Solution
A complete turn of the rectangular coil takes one second. A complete turn means a
The first change from maximum to minimum flux occurs between the
Time for one complete rotation is
Conclusion:
Therefore, the time taken for a change from maximum flux to a minimum flux is
(e)
Maximum value of voltage developed in the coil when the flux changes from a maximum to a minimum.
(e)
Answer to Problem 3SP
The maximum value of voltage developed when the flux changes from maximum value to minimum value is
Explanation of Solution
Write the equation to find the voltage developed when magnetic flux changes from maximum value to minimum value.
Here,
Substitute
Conclusion:
Therefore, the maximum value of voltage induced when flux changes from a maximum value to a minimum value is
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