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

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

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

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

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

Accepted Answer

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

Question 6

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

Accepted Answer

Find the vector sum of the electric fields produced by each charge at the center.

Question 7

Which statement about electric field lines is correct?

Accepted Answer

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

Question 8

A water molecule is electrically neutral but 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 9

What is the net force on an electric dipole placed in a uniform electric field?

Accepted Answer

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

Question 10

Which of the following equations represents the torque $	au$ on an electric dipole with dipole moment $\vec{p}$ in a uniform electric field $\vec{E}$?

Accepted Answer

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

Question 11

A charged line segment produces an electric field at a point $P$ located a distance $d$ from the segment. Which method is appropriate to calculate the electric field at $P$?

Accepted Answer

Integrate the contributions from each infinitesimal segment of charge along the line.

Question 12

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

Accepted Answer

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

Question 13

If a test charge $q_0$ experiences a force $\vec{F}_0$ at point $P$ due to another charge, what is the electric field at $P$?

Accepted Answer

$\vec{E} = \frac{\vec{F}_0}{q_0}$

Question 14

Which of the following statements about the superposition principle for electric fields is correct?

Accepted Answer

The total electric field at a point is the vector sum of the fields due to all charges.

Question 15

Why do sodium and chloride ions dissolve easily in water?

Accepted Answer

Water molecules are electric dipoles, so their positive and negative ends attract and stabilize the ions in solution.

Question 16

Which of the following is true about electric field lines for two equal positive charges placed near each other?

Accepted Answer

Field lines point away from both charges and never intersect.

Question 17

A negative point charge produces an electric field at a point $P$. In which direction does the electric field at $P$ point?

Accepted Answer

Directly toward the charge.

Question 18

Which of the following best describes the spacing of electric field lines and the magnitude of the electric field?

Accepted Answer

Closer spacing of field lines indicates a stronger electric field.

Question 19

A dipole is placed in a uniform electric field. What is the direction of the torque acting on the dipole?

Accepted Answer

The torque acts to align the dipole moment with the electric field.

Electric Charge and Electric Field – Study Notes

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