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Chapter 29: Q. 18 (page 831)

A small, square loop carries a $25 A$ current. The on-axis magnetic field strength $50 cm$ from the loop is $7.5 nT$ . What is the edge length of the square?

Short Answer

Expert verified

The edge length is $13.5 mm .$

Step by step solution

01

Given information

We have given,

Current = $25 A$

Distance = $50 cm$

Magnetic field = $7.5 nT$

We have to find the length of the edge of square.

02

Simplify

We know the magnetic field strength due to magnetic dipole moment

$B = \frac{μ_{0} \vec{μ}}{2 {πr}^{3}} \vec{μ} = \frac{2 {πr}^{3} B}{μ_{0}} \vec{μ} = \frac{2 π \times {(0.5)}^{3} \times 7.5 \times 10^{- 9}}{4 π \times 10^{- 7}} \vec{μ} = 4.6 mA . m^{2}$

Then magnetic moment for closed loop will be

$\vec{μ} = A I = L^{2} I L = \sqrt{\frac{\vec{μ}}{I}} L = \sqrt{\frac{4.6 \times 10^{- 3}}{25}} L = 13.5 m m$

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Most popular questions from this chapter

FIGURE EX29.37 is a cross section through three long wires with linear mass density 50 g/m. They each carry equal currents in the directions shown. The lower two wires are 4.0 cm apart and are attached to a table. What current I will allow the upper wire to “float” so as to form an equilateral triangle with the lower wires?

The microwaves in a microwave oven are produced in a special tube called a magnetron. The electrons orbit the magnetic field at $2.4 G H z$ , and as they do so they emit $2.4 G H z$ electro-magnetic waves.

a. What is the magnetic field strength?

b. If the maximum diameter of the electron orbit before the electron hits the wall of the tube is $2.5 c m$ , what is the maximum electron kinetic energy?

A wire along the x-axis carries current I in the negative x-direction through the magnetic field

$B = \{\begin{cases} B_{0} \frac{x}{L} \hat{k}, 0 \leq x \leq L \\ 0, elsewhere \end{cases}$

a. Draw a graph of B versus x over the interval $- \frac{3 L}{2} < x < \frac{3 L}{2}$ .

b. Find an expression for the net force ${\overset{⇀}{F}}_{net}$ on the wire.

c. Find an expression for the net torque on the wire about the point x = 0.

The heart produces a weak magnetic field that can be used to diagnose certain heart problems. It is a dipole field produced by a current loop in the outer layers of the heart.

a. It is estimated that the field at the center of the heart is $90 p T$ . What current must circulate around an $8.0 c m$ -diameter loop, about the size of a human heart, to produce this field?

b. What is the magnitude of the heart’s magnetic dipole moment.

Find an expression for the magnetic field strength at the center (point P) of the circular arc in $F I G U R E P 29.45 .$

$F I G U R E P 29.45$ localid="1649251364548" $F I G U R E P 29.46$

See all solutions

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