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### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# A certain particle is sent into a uniform magnetic field, with the particle’s velocity vector perpendicular to the direction of the field. Figure 28-37 gives the period T of the particle’s motion versus the inverseof the field magnitude B. The vertical axis scale is set by , and the horizontal axis scale is set by what is the ratio m/q of the particle’s mass to the magnitude of its charge?

The ratio m/q of the particle’s mass to the magnitude of its charge is .

See the step by step solution

## Given

Y axis scale is .

X axis scale is

Figure 28-37 is the graph of

## Determining the concept

Use the concept of the period of the particle in a uniform magnetic field. Use the equation of period related to mass, charge, and magnetic field. Find the slope of the graph and plug it intothe equation. Rearranging the equation for , find this ratio.

Formulae are as follows:

Where T is the time period, B is the magnetic field, m is mass, and q is the charge ofthe particle.

## Determining the ratio m/q

Using the equation,

Rearranging it for ,

We have the value of ,

From the graph, find the slope

For the y-axis, one unit is , and for the x-axis, one unit is

Using this value in the above equation of ,

Hence, the ratio m/q of the particle’s mass to the magnitude of its charge is .

Therefore, by using the concept of the period of the particle in a uniform magnetic field and equations the ratio can be determined.