Chapter 10: Q12 P (page 517)

$F = q (E + v \times B)$

Short Answer

Expert verified

B is an axial vector.

Step by step solution

Given information.

Physics definitions are given.

Definition of Biot-Savart law.

Define the Biot Savart law.

$B (r) = \frac{μ_{0}}{4 π} \int_{Ω} \frac{J (r^{'}) \times (r - r^{'})}{| r - r^{'} |^{3}} d^{3} r^{'}$

Write about the nature of various vectors.

F, E are polar vectors. Therefore, $V \times B$ is also a polar vector.

It is known that the vector product of a polar vector and an axial vector results in a polar vector. It is known that velocity is a polar vector. This implies that B is an axial vector.

Another method. Begin with the definition of the Biot Savart Law.

Define the Biot Savart Law.

$B (r) = \frac{μ_{0}}{4 π} \int_{Ω} \frac{J (r^{'}) \times (r - r^{'})}{| r - r^{'} |^{3}} d^{3} r^{'}$

Since J is a polar vector in this equation, write the conclusion.

$J (r') \times (r - r')$

Due to the reasoning explained above, the equation above is an axial vector.

Write the final conclusion.

Since, the above vector is an axial vector, B is an axial vector.

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!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

$F = q (E + v \times B)$

Short Answer

Step by step solution

Given information.

Definition of Biot-Savart law.

Write about the nature of various vectors.

Another method. Begin with the definition of the Biot Savart Law.

Write the final conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Measurements

Linear Momentum

Classical Mechanics

Torque and Rotational Motion

Medical Physics

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

F=q(E+v×B)

Short Answer

Step by step solution

Given information.

Definition of Biot-Savart law.

Write about the nature of various vectors.

Another method. Begin with the definition of the Biot Savart Law.

Write the final conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Measurements

Linear Momentum

Classical Mechanics

Torque and Rotational Motion

Medical Physics

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

$F = q (E + v \times B)$