Look at the drawings below. In each, the magnetic field is uniform and directed

Question

Look at the drawings below. In each, the magnetic field is uniform and directed into the page. The two circular paths show the motion of charges in the magnetic field. For each picture answer the following: a) Are the charges the same sign? Explain? If you can, determine the sign of the charge for each of the circular trajectories. b) Can the speeds of the charges be the same for the two charges? (answer for each picture) If so, are other quantities constrained, such as mass or charge? Explain. c) Can the mass of the charges be the same for the two charges? (answer for each picture) If so, are other quantities constrained, such as speed or charge?

Explanation / Answer

Radius of curvature of the path is given by R = mv/qB

(a) For the first figure since their circular motion is in same sense( both clockwise) they have same sign. Both charges have negative signs.

For second figure,their circular motion is in opposite sense they have different sign. Left charge has negative sign while right charge has positive sign.

For the third figure since their circular motion is in same sense( both anticlockwise) they have same sign. Both charges have positive sign.

(b)  R = mv/qB, if charge and mass for both charges is considered equal, then only in third figure they have same speed because they have same Radius of curvature R.

(c)  R = mv/qB, if charge and speed for both charges is considered equal, then only in third figure they have same mass because they have same Radius of curvature R.

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