Question

Figure 22-22 shows three arrangements of electric field lines. In each arrangement, a proton is released from rest at point Aand is then accelerated through point Bby the electric field. Points Aand Bhave equal separations in the three arrangements. Rank the arrangements according to the linear momentum of the proton at point B, greatest first.

Short answer

The rank of the arrangements according to the linear momentum of the proton at point B is$p_1>p_2>p_3$.

Step-by-step solution

Understanding the concept of electric field 

The linear momentum of a body depends on its mass and velocity. Here, the mass of the proton is the same in all three cases; momentum depends on the velocity of the proton, being accelerated. Thus, the more the acceleration value, the maximum the final velocity of the proton. Now, the region in which the field lines are closer has a more accelerated value than those lines that are at farther distances.

Calculation of the rank according to the linear momentum of the proton

For case (a):

The electric field lines are much closer and uniform, so the acceleration of the proton is this case is uniform till reaching point B. Hence, the proton has a maximum velocity at B, thus linear momentum$p_1$ is maximum.

For case (b):

In this case, the electric field lines are going away from each other, thus the electric field decreases continuously. Hence, the linear momentum$p_2$ is moderate at point B.

For case (c),

Here, the field lines are farthest among the three given cases. Thus, the acceleration of the proton is minimum due to the weakest electric field.

Hence, the linear momentum$p_3$ is weakest at point B

So, the rank of the arrangements on the basis of their linear momentum is$p_1>p_2>p_3$.