Question

A large positive charge pulls on a distant electron. How does the net force on the electron change if a slab of glass is inserted between the large positive charge and the electron? Does the net force get bigger, smaller, or stay the same? Explain, using only labeled diagrams. (Be sure to show all the forces on the electron before determining the net force on the electron, not just the force exerted by the large positive charge. Remember that the part of the net force on the electron contributed by the large positive charge does not change when the glass is inserted: the electric interaction extends through matter.)

Short answer

The net force on the electron will become smaller.The force on the electron in the presence of a glass slab decreases due to an opposing force (field), which is executed due to the polarization of glass.

Step-by-step solution

Concept

The force between two charges depends upon the charges, the distance between them, and the medium they are in. If the medium between them changes, the force will also change accordingly.

The change in the net force

Case 1 : In the air (vacuum)

The net force between charge Q and electron e can be written as when they are at a distance r from each other as,

${\overrightarrow{F}}_1=\frac{1}{4\pi {\epsilon }_0}\left(\frac{Qe}{r^2}\right)$

Here ${\epsilon }_0$is the permittivity of free space.

Case 2: The slab of glass

The net force between charge Q and electron e can be written as when they are at a distance r from each other when there is a slab of glass inserted as,

$$\begin{gathered} {\overrightarrow{F}}_2={\overrightarrow{F}}_1-{\overrightarrow{F}}_p \\ =\frac{1}{4\pi {\epsilon }_0{\epsilon }_r}\left(\frac{Qe}{r^2}\right) \end{gathered}$$

Here${\overrightarrow{F}}_p$is the force opposite to the attraction force due to the polarization of the slab of glass and ${\epsilon }_r$ is the relative permittivity due to the glass.

The only difference is the factor ${\epsilon }_r$ in both cases.

Thus, the net force on the electron will become smaller.The force on the electron in the presence of a glass slab decreases due to an opposing force (field), which is executed due to the polarization of glass.