Q72P 聽A circular loop has radius and... [FREE SOLUTION]

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University Physics with Modern Physics

Hugh D. Young, Roger A. Freedman

Physics

14th edition Edition 路 1596 pages

ISBN: 9780321973610

Chapter 4: Q72P (page 952)

A circular loop has radius and carries current $l_{2}$ in a clockwise direction (Fig. P28.72). The centre of the loop is a distance D above a long, straight wire. What are the magnitude and direction of the current $l_{1}$ in the wire if the magnetic field at the centre of the loop is zero?

Short Answer

Expert verified

The magnitude and direction of the current I₁ in the wire when the magnetic field at the centre of the loop is zero is $I_{1} = \frac{蟺 D}{R} I_{2}$ pointing towards the right.

Step by step solution

Concept of magnetic field due to a current-carrying loop.

The magnetic field at the centre due to a current-carrying loop is given by,

$B = \frac{渭_{0} 1}{2 R}$ 鈥�.. (1)

Here,B is the magnetic field, $渭_{0}$ is the permeability of free space, l is the current, and R is the radius.

Determination of the magnitude and direction of the current in the wire when the magnetic field at the centre of the loop is zero.

The straight long wire produces a magnetic field as below.

$B_{1} = \frac{渭_{0} I_{1}}{2 蟺 D}$

The magnetic field due to the loop referring to equation (1) is,

$B_{2} = \frac{渭_{0} I_{2}}{2 R}$

In order for the magnetic field to be zero at the given point, the magnitudes of the fields must cancel.

So,

$\begin{aligned} B = B_{1} 鈭� B_{2} \\ = 0 \\ B_{1} = B_{2} \\ \frac{渭_{0} l_{1}}{2 蟺 D} = \frac{渭_{0} I_{2}}{2 R} \end{aligned}$

Thus, solve for I₁

$I_{1} = \frac{蟺 D}{R} I_{2}$

Hence, as $l_{2}$ is directed into the page so direction of $I_{1} = \frac{蟺 D}{R} I_{2}$ is towards the right.

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91影视

A circular loop has radius and carries current $l_{2}$ in a clockwise direction (Fig. P28.72). The centre of the loop is a distance D above a long, straight wire. What are the magnitude and direction of the current $l_{1}$ in the wire if the magnetic field at the centre of the loop is zero?

Short Answer

Step by step solution

Concept of magnetic field due to a current-carrying loop.

Determination of the magnitude and direction of the current in the wire when the magnetic field at the centre of the loop is zero.

One App. One Place for Learning.

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91影视

A circular loop has radius and carries current l2in a clockwise direction (Fig. P28.72). The centre of the loop is a distance D above a long, straight wire. What are the magnitude and direction of the currentl1 in the wire if the magnetic field at the centre of the loop is zero?

Short Answer

Step by step solution

Concept of magnetic field due to a current-carrying loop.

Determination of the magnitude and direction of the current in the wire when the magnetic field at the centre of the loop is zero.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

Further Mechanics and Thermal Physics

Fundamentals of Physics

Mechanics and Materials

Translational Dynamics

Electricity

Study anywhere. Anytime. Across all devices.

A circular loop has radius and carries current $l_{2}$ in a clockwise direction (Fig. P28.72). The centre of the loop is a distance D above a long, straight wire. What are the magnitude and direction of the current $l_{1}$ in the wire if the magnetic field at the centre of the loop is zero?