Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Question
Chapter 30, Problem 29PQ

(a)

To determine

Find the magnitude and direction of the magnetic field due to the two loops at the origin.

(a)

Expert Solution
Check Mark

Answer to Problem 29PQ

The direction of the magnetic field is out of the page and magnitude of magnetic field is 1.02×105 T_.

Explanation of Solution

Assume that magnetic field due to smaller loop is B1 and magnetic field due to larger loop is B2.

Write the expression for magnetic field due to smaller loop as.

    B1=μ04π(2πi1r1)                                                                                             (I)

Here, i1 is the current, r1 is the radius and μ0 is the permeability of smaller loop. The direction of the magnetic field is inward.

Write the expression for magnetic field due to larger loop as.

    B2=μ04π(2πi2r2)                                                                                           (II)

Here, i2 is the current, r2 is the radius and μ0 is the permeability of larger loop.

The direction of the magnetic field is outward.

Write the expression for net magnetic field as.

    Bnet=B2B1

Substitute μ04π(2πi2r2) for B2 and μ04π(2πi1r1) for B1 in above equation.

Physics for Scientists and Engineers: Foundations and Connections, Chapter 30, Problem 29PQ =(μ04π)2π[i2r2i1r1]=μ0×2π4π[i2r2i1r1]

Rearrange the above equation as.

    Bnet=μ02[i2r2i1r1]                                                                                       (III)

Conclusion:

Substitute 4.00 A for i1, 9.00 A for i2, 10.0 cm for r1, 16.0 cm for r2 and 4π×107 N/A2 for μ0 in equation (III).

    Bnet=4π×107(N/A2)2[9.00 A16.0×102 m4.00 A10.0×102 m]=1.02×105 T

Thus the direction of the magnetic field is out of the page and magnitude of magnetic field is 1.02×105 T_.

(b)

To determine

Determine the radius r2 for the magnetic field at the origin to be zero.

(b)

Expert Solution
Check Mark

Answer to Problem 29PQ

The magnetic field at the origin to be zero for r2 is 0.225 m_

Explanation of Solution

When r1 is held constant at 10.0 cm, then magnetic field of smaller loop will be equal to magnetic field of larger loop.

Write the expression for the magnetic field at the origin to be zero as.

    B1=B2μ04π(2πi1r1)=μ04π(2πi2r2)

Rearrange the above equation as.

    i1r1=i2r2

Rearrange the above equation as.

    r2=i2×r1i1                                                                                                    (IV)

Here, i1 is the current, r1 is the radius i2 is the current and r2 is the radius.

Conclusion:

Substitute 4.00 A for i1, 9.00 A for i2 and 10.0 cm for r1 in equation (IV).

    r2==9.00A×10.0cm4.00A=9.00A×10.0×102m4.00A=0.225 m

Thus, the magnetic field at the origin to be zero for r2 is 0.225 m_.

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Chapter 30 Solutions

Physics for Scientists and Engineers: Foundations and Connections

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