Chapter 28, Problem 1Q

To determine

To find:

Whether the orientation of the vectors are physically reasonable.

Answer to Problem 1Q

Solution:

The orientation of vectors in figure (b) are the only physically reasonable vectors.

Explanation of Solution

1) Concept:

We can use the right hand rule to find the direction of force. For the possible orientation, we must have three vectors mutually perpendicular. From this, we can predict whether the orientation of the vectors is physically reasonable or not in the given figures.

We know that $\overrightarrow{F}= \overrightarrow{v}$ x $\overrightarrow{B}$.

2) Given:

We are given different orientation of vectors.

3) Calculations:

For fig. (a) Orientation of vectors is not possible because velocity $\overrightarrow{v}$ is not perpendicular to magnetic force $\overrightarrow{F_B}$.

For fig. (b) Orientation of vectors is possible because force $\overrightarrow{F}$ is perpendicular to velocity $\overrightarrow{V}$ and magnetic field $\overrightarrow{B}$, as according to the cross product $\overrightarrow{F}= \overrightarrow{v}$ x $\overrightarrow{B}$

For fig. (c) Orientation of vectors is not possible because $\overrightarrow{B}$ is not perpendicular to force $\overrightarrow{F_B}$.

Conclusion

Using the right hand rule we can find the direction of force, and it must be perpendicular to both velocity and magnetic field.