Question

8 (a) An object can be both charged and polarized. On a negatively charged metal ball, the charge is spread uniformly all over the surface (Figure 14.42). If a positive charge is brought near, the charged ball will polarize. If any of the following quantities is zero, state this explicitly. (1) Draw the approximate final charge distribution on the ball. (2) At the center, draw the electric field due to the external positive charge. (3) At the center, draw the electric field due to the charge on the surface of the ball. (4) At the center, draw the net electric field.

(b) Next, consider a negatively charged plastic pen that is brought near a neutral solid metal cylinder (Figure 14.43). If any of the following quantities is zero, state this explicitly. (1) Show the approximate charge distribution for the metal cylinder. (2) Draw a vector representing the net force exerted by the pen on the metal cylinder, and explain your force vector briefly but completely, including all relevant interactions. (3) At the center, draw the electric field due to the external negative charge. (4) At the center, draw the electric field due to the charge on the surface of the ball. (5) At the center, draw the net electric field.

(c) Replace the solid metal cylinder with a solid plastic cylinder. (1) Show the approximate charge distribution for the plastic cylinder. (2) Draw a vector representing the net force exerted by the pen on the plastic cylinder. (3) Explain your force vector briefly but completely, including all relevant interactions.

Short answer

(a) Due to the charge distribution, the sphere is not uniform and also the net field of the sphere is zero.

(b) The neutral metal cylinder has been polarized by the negative pen by shifting the sea of electrons. The positive charges are closer than the negative charges. The pen exerts an attraction force on the cylinder and the net field of the cylinder is zero.

(c) The neutral metal cylinder has been polarized by the negative pen by polarizing the molecules of the cylinder. The positive charges are closer than the negative charges. The pen exerts an attraction force on the cylinder and the net field of the cylinder is zero.

Step-by-step solution

Significance of the charge distribution

The charge distribution mainly composed of various charged particles that is separated by a particular region that contains no charge. However, there are three types of the charge distribution that includes linear, surface and volume charge distribution.

(a) Stating the charge distribution of the object explicitly along with the diagrams

The charge distribution is not uniform for longer period because the charge is uniformly spread all over the atom and electric field developed around it. However, it has been observed that the net electric field is zero as the positive charge is brought near. Hence, the positive charge is polarizing the negative charge.

The diagrams have been drawn below:

Thus, due to the charge distribution, the sphere is not uniform and also the net field of the sphere is zero.

(b) Stating the charge distribution of the object explicitly along with the diagrams

Negative pen polarizes the neutral metal cylinder by shifting the electron sea; the positive charges are closer than the negative charges, so the pen exerts a net attraction on the cylinder. However, it has been observed that the net electric field is zero as the negatively charged plastic pen is brought near the neutral solid metal cylinder. Hence, the changes cancel from both the ends of the sphere.

The diagrams have been provided below:

Thus, the neutral metal cylinder has been polarized by the negative pen by shifting the sea of electrons. The positive charges are closer than the negative charges. The pen exerts an attraction force on the cylinder and the net field of the cylinder is zero.

(c) Stating the charge distribution of the object explicitly along with the diagrams

Negative pen polarizes the neutral plastic cylinder by polarizing the molecules; positive charges are closer than the negative charges, so the pen exerts a net attraction on the cylinder. However, it has been observed that the net electric field is zero as the solid plastic cylinder is brought near the plastic pen. Hence, the net electric field also becomes zero as the charges cancel each other.

The diagrams have been drawn below:

Thus, the neutral metal cylinder has been polarized by the negative pen by polarizing the molecules of the cylinder. The positive charges are closer than the negative charges. The pen exerts an attraction force on the cylinder and the net field of the cylinder is zero.