Hi, I\'m close (I think) but not coming up with the correct answer. At low speed

Question

Hi, I'm close (I think) but not coming up with the correct answer.

At low speeds, a charged object in a magnetic field moves in a circular path of radius r = mv/qB. If an electron moves in an orbit of radius 10 cm with a speed of 1.0 x 10^5 m/s, what will the radius be when its speed is 0.96c? Thesqrt answer is 0.124 nm, and that isn't what I've come up with.

I solved r = mv/qB to find B = 1.456 x 10 ^-43, then tried to resolve for r with the new radius. That wasn't right, plus it didn't take into account any relativistic effect. The equation from this part of the chapter is

m = mo/ sqrt 1 - v^2/C^2. but I'm not sure where to apply it. Thanks!

Explanation / Answer

Here the speed is close to "c" therefore you have to appy the relativistic effect to get the correct answer.

Using this the new mass becomes 3.57 x mo (m = mo/ sqrt 1 - v^2/C^2)

Now you will get the answer with the above formula i.e r = mv/qB

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