(a)
The proof for the statement that the magnetic field on the axis at a distance
(a)
Answer to Problem 60AP
The proof for the statement that the magnetic field at a distance
Explanation of Solution
The following figure shows two circular coils of radius
Figure-(1)
From Figure (1) consider that the distance
Write the expression for the magnetic field at point
Here,
Write the expression for the magnetic field at point
Here,
From Figure (1) it is shown that the current is flowing on the same direction. Therefore the expression for the net magnetic field at point
Here,
Substitute
Therefore, magnetic field at a distance
(b)
The proof that
(b)
Answer to Problem 60AP
The proof that
Explanation of Solution
The magnetic field at the point midway between the coils is,
Differentiate the above equation with respect to
Substitute
Differentiate Equation (II) with respect to
Substitute
Further solve the above equation.
Conclusion:
From Equation (III) and Equation (IV),
Therefore, both the coils are Helmholtz coils.
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Chapter 30 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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