Q: Which Maxwell equation relates the electric field to the charge density in electrostatics?

$\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0}$

Q: Which formula gives the torque $\tau$ on an electric dipole with moment $\vec{p}$ in a uniform electric field $\vec{E}$?

$\tau = \vec{p} \times \vec{E}$

Question 1

Which of the following best describes the difference between electric force and electric field?

Accepted Answer

Electric field is a property of space created by a charge, while electric force is the interaction experienced by a charge placed in that field.

Question 2

According to Coulomb's Law, what happens to the magnitude of the electric force between two point charges if the distance between them is doubled?

Accepted Answer

The force decreases by a factor of 4.

Question 3

Which equation correctly expresses Coulomb's Law for the magnitude of the electric force between two point charges?

Accepted Answer

$F = k \frac{|q_1 q_2|}{r^2}$

Question 4

A positive test charge is placed in an electric field produced by a negative point charge. In which direction does the force on the test charge point?

Accepted Answer

Toward the negative charge.

Question 5

Which of the following statements about electric field lines is TRUE?

Accepted Answer

The tangent to an electric field line at any point gives the direction of the electric field vector at that point.

Question 6

A water molecule is electrically neutral overall, but it acts as an electric dipole. What causes this dipole behavior?

Accepted Answer

The chemical bonds within the molecule cause a displacement of charge, resulting in a net negative charge on the oxygen end and a net positive charge on the hydrogen end.

Question 7

Which of the following is the correct vector equation for the electric field produced by a point charge $q$ at a distance $r$?

Accepted Answer

$\vec{E} = k \frac{q}{r^2} \hat{r}$

Question 8

If three point charges are placed at the vertices of an equilateral triangle, how do you determine the net electric field at the center of the triangle?

Accepted Answer

Add the vector electric fields from each charge using superposition.

Question 9

Which Maxwell equation relates the electric field to the charge density in electrostatics?

Accepted Answer

$
abla \cdot \vec{E} = \frac{ho}{\varepsilon_0}$

Question 10

A dipole is placed in a uniform electric field. What is the net force and torque on the dipole?

Accepted Answer

The net force is zero, but there can be a nonzero torque.

Question 11

Which formula gives the torque $	au$ on an electric dipole with moment $\vec{p}$ in a uniform electric field $\vec{E}$?

Accepted Answer

$	au = \vec{p} 	imes \vec{E}$

Question 12

Why is water a good solvent for ionic compounds like salt?

Accepted Answer

Water molecules are electric dipoles, so they attract and stabilize both positive and negative ions in solution.

Question 13

Which statement about electric field lines for two equal positive charges is correct?

Accepted Answer

Field lines never intersect and point away from both charges.

Question 14

A charged line segment produces an electric field at a point P. Which principle is used to calculate the total electric field at P?

Accepted Answer

The principle of superposition, summing the vector fields from each infinitesimal charge element.

Question 15

If a negative point charge is placed at the origin, what is the direction of the electric field at a point on the positive x-axis?

Accepted Answer

Toward the origin.

Question 16

A test charge $q_0$ is placed at a point where the electric field is $\vec{E}$. What is the force experienced by the test charge?

Accepted Answer

$\vec{F} = q_0 \vec{E}$

Question 17

Which of the following best describes the behavior of electric field strength as the distance from a point charge increases?

Accepted Answer

It decreases as the inverse square of the distance.

Question 18

A dipole consists of charges $+q$ and $-q$ separated by distance $d$. What is the magnitude of its dipole moment?

Accepted Answer

$p = qd$

Question 19

Which of the following is a real-world consequence of water molecules being electric dipoles?

Accepted Answer

Water can dissolve salts and support aqueous chemistry essential for life.

Electric Charge and Electric Field: Study Notes (Chapter 21, University Physics)

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