Question

Un haz de electrones se dirige a un campo magnético uniforme y se desvía como se muestra en la Figura I. Si un haz de protones con la misma velocidad entrara en este mismo campo magnético, ¿Cuál de las trayectorias que se muestran en la Figura Il tomarían los protones? Figure Figure 11 electron beam proton beam uniform ] uniform 1 2

An electron beam is directed into a uniform magnetic field and deviates as shown in Figure I. If a proton beam with the same velocity entered this same magnetic field, which of the paths shown in Figure II would they take the protons?

Answer 1

Answer - Path 2 is the correct answer

Explanation

When the charged particles beam enters in the magnetic field, the beam will experience Lorentz force. the Lorentz force is given by

F = qv X B

Where q is the charge, v velocity and B is the uniform magnetic field.

In the case of Electron beam q = -e then Lorentz force is given by F= -e (vxB), this force acting downward as shown in figure 1  in case of the electron beam.

Now we take when the proton beam with the same velocity enters into the magnetic field, the Lorentz force is given by, F= e(vxB) because of q= e for proton. In the case of proton Lorentz force act on the beam upward.

In figure II there are two paths of the different radius of curvature,  which are going upward. The path  1 having a radius of curvature equal to the radius of curvature of electron path in figure 1 and path  2 has different value radius of curvature.

The radius of curvature is defined by

r = my2 E qvВ mv qB

From the above equation, we can say that for the uniform magnetic field, the radius of curvature is directly proportional mass. in case of proton radius of curvature more because proton has more mass than an electron(m_p>m_e)

So path 2 is the correct answer

thank you !!