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Chapter 10: Q12 P (page 517)

F=q(E+v脳B)

Short Answer

Expert verified

B is an axial vector.

Step by step solution

01

Given information.

Physics definitions are given.

02

Definition of Biot-Savart law.

Define the Biot Savart law.

B(r)=渭04蟺鈭�惟J(r')脳(r-r')|r-r'|3d3r'

03

Write about the nature of various vectors.

Write about the nature of various vectors.

F, E are polar vectors. Therefore,V脳Bis 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.

04

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

Define the Biot Savart Law.

B(r)=渭04蟺鈭�惟J(r')脳(r-r')|r-r'|3d3r'

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

J(r')脳(r-r')

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

05

Write the final conclusion.

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

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Most popular questions from this chapter

If P and S are 2nd-rank tensors, show that 92=81coefficients are needed to write each component of P as a linear combination of the components of S. Show that 81=34is the number of components in a 4th-rank tensor. If the components of the 4th -rank tensor are Cijkm , then equation gives the components of P in terms of the components of S. If P and S are both symmetric, show that we need only 36different non-zero components inCijkm . Hint: Consider the number of different components in P and S when they are symmetric. Comment: The stress and strain tensors can both be shown to be symmetric. Further symmetry reduces the 36components of C in (7.5)to 21or less.

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