Learning Goal: To understand Coulomb\'s law, electric fields, and the connection

Question

Learning Goal:

To understand Coulomb's law, electric fields, and the connection between the electric field and the electric force.

Coulomb's law gives the electrostatic force F acting between two charges. The magnitude F of the force between two charges q1 and q2 depends on the product of the charges and the square of the distance r between the charges:

F=k|q1q2|r2,

where k=1/(40)=8.99×109Nm2/C2. The direction of the force is along the line connecting the two charges. If the charges have the same sign, the force will be repulsive. If the charges have opposite signs, the force will be attractive. In other words, opposite charges attract and like charges repel.

Because the charges are not in contact with each other, there must be an intermediate mechanism to cause the force. This mechanism is the electric field. The electric field at any location is equal to the force per unit charge experienced by a charge placed at that location. In other words, if a charge qexperiences a force F , the electric field E  at that point is

E =F q.

The electric field vector has the same direction as the force vector on a positive charge and the opposite direction to that of the force vector on a negative charge.

An electric field can be created by a single charge or a distribution of charges. The electric field a distance r from a point charge q has magnitude

E=k|q|r2.

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 q 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).

Part A

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.

Check all that apply.

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Part B

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.

Check all that apply.

the distance between the positive charge and the electron the charge on the electron the mass of the electron the charge of the positive charge the mass of the positive charge the radius of the positive charge the radius of the electron

Explanation / Answer

Part A:

according to coulomb's law

F = k q1 q2/r2

r = distance between charge and the electron

q1 = charge of positive charge

q2 = charge of electron

Part B)

electric field at the location of electron is given as

E = kq1/r2

r = distance between charge and the electron

q1 = charge of positive charge

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