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29. Sources of Magnetic Field

Magnetic Field Produced by Loops and Solenoids

29. Sources of Magnetic Field

Magnetic Field Produced by Loops and Solenoids

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Magnetic Field Produced by Loops and Solenoids

Find How Many Loops in a Solenoid

Designing a Solenoid (Total Length of Wire)

Find Magnetic Field By Two Concentric Loops

Practice this topic

Multiple Choice

The single loop below has a radius of 10 cm and is perpendicular to the page (shown at a slight angle so you can better visualize it). If the magnetic field at the center is 10^-6 T directed left, what is the magnitude of the current? What is the direction of the current at the top of the wire:into the page (towards left) or out of the page (towards right)?

Has a video solution.

Multiple Choice

A long wire having total resistance of 10 Ω is made into a solenoid with 20 turns of wire per centimeter. The wire is connected to a battery, which provides a current in order to produce a 0.04 T magnetic field through the center of the solenoid. What voltage must this battery have?

Has a video solution.

The two tightly wound solenoids below both have length 40 cm and current 5 A in the directions shown. The left solenoid has radius 20 cm and 50 m of total wire. The right solenoid has radius 0.5 m and 314 m of total wire. The thinner solenoid is placed entirely inside the wider one so their central axes perfectly overlap. Assume wires don't touch. What is the magnitude and direction of the magnetic field that is produced by a combination of the two solenoids at their central axis?

(Note:your worksheet may have a typo and say "0.5 cm"for the right solenoid's radius; it should be 0.5 m.)

Has a video solution.

Multiple Choice

A certain solenoid is

30 cm

long and has 1500 turns of wire. If the magnetic field inside the solenoid is

30 mT

, what is the current in the wire?

Multiple Choice

A loop of wire has a magnetic dipole moment of

0.80 A m^{2}

_. What is the on-axis magnetic field strength

7.0 cm

Multiple Choice

A square loop of wire with

12 cm

on a side carries a

10 A

current. What is the size of its magnetic dipole moment?

Textbook Question

A solenoid is designed to produce a magnetic field of 0.0270 T at its center. It has radius 1.40 cm and length 40.0 cm, and the wire can carry a maximum current of 12.0 A. (b) What total length of wire is required?

Has a video solution.

Textbook Question

A solenoid is designed to produce a magnetic field of 0.0270 T at its center. It has radius 1.40 cm and length 40.0 cm, and the wire can carry a maximum current of 12.0 A. (a) What minimum number of turns per unit length must the solenoid have?

Has a video solution.

Textbook Question

A 15.0-cm-long solenoid with radius 0.750 cm is closely wound with 600 turns of wire. The current in the windings is 8.00 A. Compute the magnetic field at a point near the center of the solenoid.

Has a video solution.

Textbook Question

FIGURE CP29.79 is an edge view of a 2.0 kg square loop, 2.5 m on each side, with its lower edge resting on a frictionless, horizontal surface. A 25 A current is flowing around the loop in the direction shown. What is the strength of a uniform, horizontal magnetic field for which the loop is in static equilibrium at the angle shown?

Textbook Question

b. Determine the field strength at the center of a current-carrying square loop having sides of length 2R.

Textbook Question

A long, straight conducting wire of radius R has a nonuniform current density J = J₀r/R, where J₀ is a constant. The wire carries total current I. b. Find an expression for the magnetic field strength inside the wire at radius r.

Textbook Question

A 100 A current circulates around a 2.0-mm-diameter superconducting ring. a. What is the ring's magnetic dipole moment?

Textbook Question

A 100 A current circulates around a 2.0-mm-diameter superconducting ring. b. What is the on-axis magnetic field strength 5.0 cm from the ring?

Textbook Question

Each turn of a solenoid is a current loop with a magnetic dipole moment. Consider a 200-turn cylindrical solenoid that has an interior volume of 40 cm³ and for which each turn is a magnetic dipole moment with magnitude 8.0 x 10⁻⁴ A m². What is the magnetic field strength inside the solenoid?

Textbook Question

The earth's magnetic field, with a magnetic dipole moment of 8.0 x 10²² A m², is generated by currents within the molten iron of the earth's outer core. Suppose we model the core current as a 3000-km-diameter current loop made from a 1000-km-diameter 'wire.' The loop diameter is measured from the centers of this very fat wire. b. What is the current density J in the current loop?

Textbook Question

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

Textbook Question

A flat, circular disk of radius R is uniformly charged with total charge Q. The disk spins at angular velocity ω about an axis through its center. What is the magnetic field strength at the center of the disk?

Textbook Question

In FIGURE P31.32, a circular loop of radius r travels with speed v along a charged wire having linear charge density λ. The wire is at rest in the laboratory frame, and it passes through the center of the loop. d. What electric and magnetic fields would an experimenter in the loop's frame calculate at distance r from the current of part c?

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