# Electron accelerated through a potential and magnetic field

## Homework Statement

(a) What voltage will accelerate electrons to a speed of ##6.00 \times 10^{-7} m/s## ? (b) Find the radius of curvature of the path of a proton accelerated through this potential in a 0.500-T field and compare this with the radius of curvature of an electron accelerated through the same potential.

## Homework Equations

$$r=\frac{mv}{qB} \\ q\Delta V = \Delta U \\ K = \frac{1}{2}mv^2 = -\Delta U$$

## The Attempt at a Solution

For the first part I used the second equation and set it equal to the kinetic energy, K. This gave a potential difference of ##1.02 \times 10^{-24} V##. Then for the b), I used the first equation to solve for ##r = |-6.82 \times 10^{-18}| = 6.82 \times 10^{-18}##. Though I was unsure of how to solve for the radius of curvature when accelerated through the same potential, nor how to compare the two values. Also, should the r value been negative, or am I missing a negative sign in one of the values?

kuruman
Homework Helper
Gold Member
The speed of the electron looks awfully small. Are you sure of the exponent? The radius should be positive. Also, although you do not mention it, you may have assumed that the proton has the same speed as the electron. That is not true. If the proton is accelerated by the same voltage as the electron, what quantity do they have in common?

From the problem, it does have a negative, though it could be a type (it would not be the first one if it is).

So I would have to solve for the velocity of the proton using the potential solved from the first part. I solve for ##v = 1.4 \times 10^{-8} m/s## Then I would use that to solve for the radius of curvature of the proton ##r_p = 9.73 \times 10^{-17} m##. Similarly, I used the values for the electron to solve for ##r_e = 2.27 \times 10^{-18} m##. Would I just subtract ##r_p - r_e## to compare them?

Also, for the radius of curvature of the electron, what value other than q be negative so that the signs cancel to get a positive radius? Would the velocity be negative?