Chapter 31, Problem 2PQ

Review Suppose you want to use a small, positively charged ball suspended by a light thread to map out the electric field in the space around a charged source. Describe the reaction of the ball as you place it at the two locations in front of the infinitely large, positively charged sheet shown in Figure P31.2A. Be sure to relate your description to what you know about the sheet’s electric field.

To determine

The reaction of the ball at the two different locations.

Answer to Problem 2PQ

The ball will deflect same in both the cases.

Explanation of Solution

Write the expression for the electric field due to a infinite sheet of charge as.

  $E=\frac{\sigma }{2{\epsilon }_0}$                                                                                                      (I)

Here, $E$ is the electric field, ${\epsilon }_o$ is the permittivity of free space and $\sigma$ is the charge density of sheet.

Write the expression for the force on the positively charged ball as.

  $F=qE$                                                                                                      (II)

Here, $F$ is the force on charged ball and $q$ is the amount of charge.

Conclusion:

The ball is of the same charge as of the sheet. So, there will be repulsion of ball and ball will deflect away from the sheet.

Substitute $\frac{\sigma }{2{\epsilon }_0}$ for $E$ in equation (II).

  $F=q\frac{\sigma }{2{\epsilon }_0}$

The electric field at the point nearer to the sheet will be same as the electric field at the point away from the sheet as it is independent of the distance of the charged ball from the sheet.

Thus, the ball will deflect same in both the cases.