Two circular coils of radius R, each with N turns, are perpendicular to a common axis. The coil centers are a distance R apart. Each coil carries a steady current I in the same direction as shown in Figure P29.38. (a) Show that the magnetic field on the axis at a distance x from the center of one coil is
(a)
To show: The magnetic field on the axis at a distance
Answer to Problem 38AP
Hence, the magnetic field on the axis at a distance
Explanation of Solution
Given information: The radius of each coil is
Let consider a point at
Formula to calculate the magnetic field at a point due to first circular coil is,
Here,
Formula to calculate the magnetic field to the same point due to second circular coil is,
Here,
Write the expression for the net field at the given point.
Substitute
Simplify the above equation for
Conclusion:
Therefore, the magnetic field on the axis at a distance
(b)
To show: The value of
Answer to Problem 38AP
Hence, the value of
Explanation of Solution
Given information: The radius of each coil is
From equation (3), the expression for the net magnetic field is given by,
Differentiate the above equation with respect to
Substitute
Thus, the value of value of
Differentiate the equation (4) with respect to
Substitute
Thus, the value of value of
Conclusion:
Therefore, the value of
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