Question

An electric field can be created by a single charge or a distribution of charges. The electric field a distance from a point charge has magnitude E = k|q'|/r^2.

The electric field points away from positive charges and toward negative charges. A distribution of charges creates an electric field that can be found by taking the vector sum of the fields created by individual point charges. Note that if a charge is placed in an electric field created by q', q will not significantly affect the electric field if it is small compared to q'.

Imagine an isolated positive point charge with a charge Q (many times larger than the charge on a single electron).

There is a single electron at a distance from the point charge. On which of the following quantities does the force on the electron depend?
Check all that apply.
A the distance between the positive charge and the electron
B the charge on the electron
C the mass of the electron
D the charge of the positive charge
E the mass of the positive charge
F the radius of the positive charge
G the radius of the electron
I got A, B, and D for this part of the problem and was correct. However,
For the same situation as in Part A, on which of the following quantities does the electric field at the electron's position depend?
Check all that apply.
A the distance between the positive charge and the electron
B the charge on the electron
C the mass of the electron
D the charge of the positive charge
E the mass of the positive charge
F the radius of the positive charge
G the radius of the electron
I am not sure about this question. Please help!

Answer 1

Concept and reason:

The concept behind this question is coulomb’s law. Use coulomb’s law to find the electrostatic force between two charges.

First write the expression for the Coulomb’s force between the electron and the charge Q. Calculate the dependence of the force on the all parameters.

Finally, write the expression for the Electric field due to the charge Q at the electron’s position. Calculate the dependence of the electric field on the all parameters.

Fundamentals:

The expression for the Coulomb’s force between the electron and the charge Q is,

$F = \frac{1}{{4\pi {\varepsilon _{\rm{o}}}}}\frac{{\left( e \right)\left( Q \right)}}{{{r^2}}}$

Here, e is the electron charge, Q is the positive charge, ${\varepsilon _{\rm{o}}}$ is the permittivity of the free space, and r is the distance between the positive charge and the electron.

The expression for the electric field due to the charge Q is given by,

$E = \frac{1}{{4\pi {\varepsilon _{\rm{o}}}}}\frac{Q}{{{r^2}}}$

The expression for the Coulomb’s force between the electron and the charge Q is given by,

$F = \frac{1}{{4\pi {\varepsilon _{\rm{o}}}}}\frac{{\left( e \right)\left( Q \right)}}{{{r^2}}}$

The Coulomb’s force is inversely proportional to the distance between the positive charge and the electron.

From the above equation, it can also be concluded that the electric force between the charge and the electron is directly proportional to the magnitude of point charge and as well as the magnitude of electron charge and also the product of both the charges.

The expression for the electric field at the electron’s position due to the charge Q is given by,

$E = \frac{1}{{4\pi {\varepsilon _{\rm{o}}}}}\frac{Q}{{{r^2}}}$

From the above expression, it can be concluded that the electric field directly proportional to the magnitude of the charge on the given point charge, inversely proportional to the square of the distance of the point where the electric field strength is to be found.

Ans:

The electric force between the on the electron depends on the distance between the positive charge and the electron, the charge of the electron and also depends on the charge on the positive charge.