When a charged particle enters a region of uniform magnetic field it follows a c

Question

When a charged particle enters a region of uniform magnetic field it follows a circular path, as indicated in the figure. (a) Is this particle positively or negatively charged? negative positive

Explain.

(b) Suppose that the magnetic field has a magnitude of 0.150 T, the particle's speed is 6.0 ? 106 m/s, and the radius of its path is 125.3 cm. Find the mass of the particle, given that its charge has a magnitude of 1.60 ? 10?19 C. Give your result in atomic mass units, u, where 1 u = 1.67 ? 10?27 kg. u

Explanation / Answer

a) Lorentz force will act on charge particle in this case given by F = q.(v x B). Lets take the direction of B into the paper given by cross circles in the figure. Assume it to be - z direction. As it can be seen that particle is moving in clockwise direction. According to right hand thumb rule, if thumb is in direction of magnetic field then curl of fingers gives the direction of force. In this case particle is moving in the direction of the curl, so it is positive in nature other wise the direction of circle would be anti clockwise if the charge would be negative..

b) Lorentz force will be balanced by centripital force given by qvB = mv2/r . Rearranging the terms will give m = qBr/v = (1.60 x 10-19 x 6.0 x 106 x .150) / 1.253 (everything in SI units) = 68 x 1012 u

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