Chapter 22, Problem 1Q

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

Figure 22-22 Qustion 1.

To determine

To rank:

The given situations according to the linear momentum of a proton released from rest in an electric field at point A.

Answer to Problem 1Q

Solution:

(a)> (b)> (c).

Explanation of Solution

1) Concept:

Electric field strength is directly proportional to the density of field lines. Hence, the field is stronger when the lines are closely located and weaker when the lines are farther away.  According to Newton’s second law, the rate of change of linear momentum of a body depends on the force acting on the body. Hence, the stronger the electric field, greater the force will be and also greater the linear momentum will be.

2) Formulae:

Electric field strength, $E\infty \frac{1}{r^2}$.

3) Given:

A proton is released from rest at point A and is then accelerated through point B.

4) Calculations:

Let us look at the given situations.

In case a, the field lines are closely located than in case b and c. Therefore the linear momentum of proton at B is greatest in case a.

In case b, the field lines are diverging from A towards B.  In C the distance between field lines are farther than in case b and c. Therefore the electric field is greater in case b than in case c. Thus momentum of proton is greater in case b than case c.

Conclusion:

Using the relationship between linear momentum and force of a particle we can compare the momentum in the given scenarios.