Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

A particle with charge 7.80 μC is moving with velocity v=-(3.80×103m/s)j^. The magnetic force on the particle is measured to be (7.60×10-3N)i^-(5.20×10-3N)k^.(a) Calculate all the components of the magnetic field you canfrom this information. (b) Are there components of the magneticfield that are not determined by the measurement of the force?Explain. (c) Calculate the scalar productBF what is the angle between Bands F?

Short Answer

Expert verified
  1. Magnetic field along x axis isBx=-0.175T and along z axis isBz=-0.256T
  2. The y component is not determined, since there is no force along this component hence measurement doesn’t tell us anything aboutBy

c. The angle between the two is 90 degrees

Step by step solution

01

The significance of the magnetic field

The magnetic field force is given by

FB=q(v×B)F=qvBsinθ

Where q is the charge of the particle, V is the velocity and B is the magnetic field

02

Determination of the components of the magnetic field

We know that the magnetic field force is given by

F=q(v×B)

We know

F=qdeti^j^k^vxvyvzBxByBzFxi^+Fyj^+Fzk^=qvyBzvzByi^+qvzBxvxBzj^+qvxByvyBxk^

We knowVx=0 thatVz=0

Fxi^+Fyj^+Fzk^=qvyBzi^-qvyBxk^

Comparing we get

Fx=qvyBzFy=0Fz=qvyBx

Substitute all the value in the above equation.

Solve for the magnetic field components

Bz=Fxqvy=7.60×103N7.80×106C×3.80×103m/s=0.256TBx=Fzqvy=5.20×103N7.80×106C×3.80×103m/s=0.175T

Hence, Magnetic field along x axis isBx=-0.175T and along z axis is Bz=-0.256T.

03

Determination of the scalar product

We see

BF=BxFx+ByFy+BzFzBF=(0.175T)7.60×103N+(0.256T)5.20×103NBF=0

This means that the two vectors are perpendicular to each other, so the angle is 90 degrees.

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.

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

A circular area with a radius of6.50cmlies in the xy-plane. What is the magnitude of the magnetic flux through this circle due to a uniform magnetic fieldlocalid="1655727900569" B=0.230T(a) in the direction of +z direction; (b) at an angle of53.1°from the direction; (c) in the direction?

In the circuit shown in Fig. E25.30, the 16.0-V battery is removed and reinserted with the opposite polarity, so that its negative terminal is now next to point a. Find (a) the current in the circuit (magnitude anddirection); (b) the terminal voltage Vbaof the 16.0-V battery; (c) the potential difference Vacof point awith respect to point c. (d) Graph the potential rises and drops in this circuit (see Fig. 25.20).

A typical small flashlight contains two batteries, each having an emf of1.5V, connected in series with a bulb having resistance17Ω. (a) If the internal resistance of the batteries is negligible, what power is delivered to the bulb? (b) If the batteries last for1.5hwhat is the total energy delivered to the bulb? (c) The resistance of real batteries increases as they run down. If the initial internal resistance is negligible, what is the combined internal resistance of both batteries when the power to the bulb has decreased to half its initial value? (Assume that the resistance of the bulb is constant. Actually, it will change somewhat when the current through the filament changes, because this changes the temperature of the filament and hence the resistivity of the filament wire.)

The tightly wound toroidal solenoid is one of the few configurations for which it is easy to calculate self-inductance. What features of the toroidal solenoid give it this simplicity?

An electron at point in figure has a speed v0=1.41×106m/s. Find (a) the magnetic field that will cause the electron to follow the semicircular path from to and (b) The time required for the electron to move fromAtoB.

See all solutions

Recommended explanations on Physics Textbooks

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