Question

Hi, I'm having a problem with finding a unit of a slope for the given function: y=(1/2)((L^2eB)/(mv)). (y is a deflection(meters), e is the charge of an electron, L is a distance (meters), m is the mass of an electron, and v is the velocity). Here, magnetic field, B, is the only variable and everything else is a constant. If so, what should be the unit for the slope?

Answer 1

Usually the slope is defined as

dy de

Where

y = f(2)

Here x is the independent variable and y is the dependent variable. If let us say that the unit of x is some X and unit if y is some Y, then the unit of slope is the ratio between Y and X. In your case you have magnetic field as a dependent variable and deflection as a independent variable. Now the slope of this can be found by evaluating

$\frac{dy}{dB}$

In this the unit of numerator is meter and that of denominator is Tesla. So the unit of slope is just the ratio between these two. It is given by

meter/Tesla

This is the answer.