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## Homework Statement

Hydrogen ions moving at various speeds are directed at a region of combined electric and magnetic fields as shown in the diagram below. The electric field is between two parallel plates 10 mm apart with a potential difference V across them, while the magnetic field of flux density 0.1 T is at right angles to the electric field.

(a) Calculate the value of V required so that ions of speed 100 m s

^{-1}pass through the region of the two fields without being deviated.

(b) What is the kinetic energy per ion as they leave the combined fields?

(1 u = 1.67 * 10

^{-27}kg.)

Answers: (a) 0.1 V, (b) 8.4 * 10

^{-24}J.

**2. The attempt at a solution**

(a) Can't get it right. I use 0.5 m v

^{2}= e V, where we don't know the mass m. I then tried to use F = B e v = 0.1 * 1.6 * 10

^{-19}* 100 = 1.6 * 10

^{-18}N and then F = m g so m = F / g = 1.6 * 10

^{-18}/ 10 = 1.6 * 10

^{-19}kg -- not correct.

I also used B e v = m v

^{2}/ r so m = B e r / v = 0.1 * 1.6 * 10

^{-19}* 0.01 / 100 = 1.6 * 10

^{-24}kg. Also not correct.

I even thought that since we have hydrogen then its relative atomic mass is 1.008 and so 1.008 * 1.67 * 10

^{-27}= 1.68 * 10

^{-27}kg, also not correct.

If we plug in 0.1 V (which we need to find) into the first formula we'll get m = 3.2 * 10

^{-24}kg. But I've got no idea how to find it.

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