Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q4P (page 222)

Suppose that the magnetic field in some region has the form

B→=kzx⏜

(where kis a constant). Find the force on a square loop (side a),lying in the yz

plane and centered at the origin, if it carries a current I,flowing counterclockwise,

when you look down the xaxis.

Short Answer

Expert verified

The force on a square loop of side a,lying in the yzplane and centered at the origin, carrying a current I,flowing counterclockwise in the presence of a magnetic fieldB→=kzx⏜ is Ia2kz⏜.

Step by step solution

01

Given data

There is a magnetic field of the formB→=kzx⏜ .

There is a square loop of side alying in the yzplane, centered at the origin and carries a current I,flowing counterclockwise.

02

Force on a current carrying wire in a magnetic field

The force on a wire carrying current I, length Iin a magnetic fieldBis

F→=||→×B→......(1)

03

Force on the current carrying loop

The force on y=a/2and y=-a/2wires are exactly equal and opposite and so they cancel out.

From equation (1), force on the z=a/2 wire

F→1=IaB\z-a/2z⏜=Iaka2z⏜=Ia2k2z⏜

From equation (1), force on the z=-a/2 wire

F→2=IaB\z-a/2-z⏜=Iak-a2-z⏜=Ia2k2z⏜

Thus, the net force on the wire is Ia2kz⏜ .

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Analyze the motion of a particle (charge q, massm ) in the magnetic field of a long straight wire carrying a steady current I.

(a) Is its kinetic energy conserved?

(b) Find the force on the particle, in cylindrical coordinates, withI along thez axis.

(c) Obtain the equations of motion.

(d) Supposez. is constant. Describe the motion.

Find the magnetic vector potential of a finite segment of straight wire carrying a current I.[Put the wire on the zaxis, fromz1 to z2, and use Eq. 5.66.]

Check that your answer is consistent with Eq. 5.37.

Question: Use Eq. 5.41 to obtain the magnetic field on the axis of the rotating disk in Prob. 5.37(a). Show that the dipole field (Eq. 5.88), with the dipole moment you found in Prob. 5.37, is a good approximation if z>> R.

Calculate the magnetic force of attraction between the northern and southern hemispheres of a spinning charged spherical shell.

A plane wire loop of irregular shape is situated so that part of it is in a uniform magnetic field B (in Fig. 5.57 the field occupies the shaded region, and points perpendicular to the plane of the loop). The loop carries a current I. Show that the net magnetic force on the loop isF=IBω, whereωis the chord subtended. Generalize this result to the case where the magnetic field region itself has an irregular shape. What is the direction of the force?
See all solutions

Recommended explanations on Physics Textbooks

Particle Model of Matter

Read Explanation

Measurements

Read Explanation

Physical Quantities And Units

Read Explanation

Linear Momentum

Read Explanation

Oscillations

Read Explanation

Magnetism

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free