Question

A small glass ball is rubbed all over with a small silk cloth and acquires a charge of +5nC. The silk cloth and the glass ball are placed 30 cm apart.

(a) On a diagram like that shown in Figure 14.71, draw the electric field vectors qualitatively at the locations marked ×. Pay careful attention to directions and to relative magnitudes. Use dashed lines to explain your reasoning graphically, and draw the final electric field vectors with solid lines.

(b) Next, a neutral block of copper is placed between the silk and the glass.

On a diagram like that shown in Figure 14.72, carefully show the approximate charge distribution for the copper block and the electric field vectors inside the copper at the locations marked ×.

(c) The copper block is replaced by a neutral block of plastic. Carefully show the approximate molecular polarization of the plastic block at the locations marked × in Figure 14.73.

(d) Even if you have to state your result as an inequality, make as quantitative a statement as you can about the electric field at the location of the glass ball and the net force on the ball when the plastic block is in place compared to when there is no block. Explain briefly.

Short answer

(a)

(b)

(c)

(d)The electric field at the location of the glass ball would be zero and the net electric force on the ball in the presence of the plastic block is lesser in compared to when there is no block.

Step-by-step solution

Understanding about the electric field

In this problem, the concept of the electric field at a specific point due to a specific electric charge will be used to evaluate the electric field's direction. The electric field depends on the electric charge’s nature.

(a) Representation of electric field vectors

When the small glass ball is rubbed with a small silk cloth, then the glass ball will acquire an electric charge as, and the small silk cloth will acquire charge.

The representation of electric field vectors qualitatively at the marked location is given below.

The solid lines represent the final electric field vectors, and a dashed line represents the magnetic field vectors at every marked location.

Thus, the magnetic field vectors at the marked location are represented by the dashed lines, and solid lines represent the final electric field vector.

(b) Representation of the approximate charge distribution for the copper block and the electric field vectors inside the copper block

A neutral copper block is placed between the silk cloth and the glass ball then, the copper block's surface closer to the glass ball would be charged as positive, and the surface of the copper block close to the silk cloth would be charged as negative.

The approximate charge distribution for the copper block and the electric field vectors inside the block is represented below.

All the electric charges lie on the copper block's outer surface, so the electric field inside the conductor will be zero, and no electric field vector exists inside the copper block at the marked locations.

Thus, the electric field vectors inside the copper block at the marked locations don’t exist.

(c) Representation of the approximate molecular polarization of the plastic block

Now the copper block is replaced by a neutral block of plastic then the surface of the plastic block closure to the glass ball would be charged as positive whereas the surface of the plastic block closure to the silk cloth would be charged as negative.

The approximate molecular polarization of the plastic block at the marked location inside the plastic block is given below.

The approximate molecular polarization at the marked location inside the plastic block is represented by the solid lines with an arrow.

Thus, the approximate molecular polarization inside the plastic block is directed towards the negative charge side (towards silk cloth).

(d) Comparison of the net electric force on the ball when the plastic ball is in place compared to when there is no block   

When there is a plastic block in place compared to when there is no block, then the external electric field polarizes the plastic block, and it results in the field being intensely reduced. Theelectric field at the location of the glass ballwould be zero.

The net electric force on the ball would be less in comparison to when there is no block (only air exists) because the plastic block would offer extra resistance that is absent when there is no block.

Thus, the net electric force on the ball in the presence of the plastic block is lesser in compared to when there is no block.