Radius of a circle with a magnetic field and electron velocity

[skibum143]

Homework Statement

An electron moving perpendicular to a magnetic field of 2.2*10^-2 T moves in a circle of certain radius. If the electron is moving with a speed of 1.5*10^7 m/s, what is the radius of the circle?

Homework Equations

B field = u0*I / 2 pi r
F = qvB

The Attempt at a Solution

I'm confused about how to find the current I in order to solve for the radius. I know that F = (-1.9*10^-19)*(1.5*10^7)*(2.2*10^-2) = -6.27*10^-10 (but positive because magnitude), but I can't figure out how to solve for r with two unknowns (r and I). Can someone help?

Thanks!

 

[rock.freak667]

The electron moves in a circle, so that the magnetic force is providing (equals) the centripetal force.

 

[collinsmark]

Hello skibum143,

I'm confused about how to find the current I in order to solve for the radius.

Um, why are you solving for I? There are no wires carrying current involved in this problem (well, none that we know about anyway). You already know the magnetic field (it's given in the problem statement), so there's no need to calculate that.

I know that F = (-1.9*10^-19)*(1.5*10^7)*(2.2*10^-2) = -6.27*10^-10 (but positive because magnitude),

The charge of an electron is -1.602 x 10^-19 C, btw. Be careful of your exponents too.

but I can't figure out how to solve for r with two unknowns (r and I). Can someone help?

Well, you have the capability of finding a force on the electron. The magnetic force (in this problem) is perpendicular to the electron's instantaneous velocity, such that it travels in a circle. The electron's speed is given in the problem statement. Can you think of any equation that relates force, velocity and radius of things traveling in a circle?

[Edit] Hint. You can always look up the mass of an electron if you need to.

 

[skibum143]

I see, thank you!