Q: Which equation represents the cross product of two vectors $\vec{A}$ and $\vec{B}$?

$\vec{A} \times \vec{B} = (A_x B_y - A_y B_x) \hat{k}$

Question 1

Which of the following statements best describes the relationship between electricity and magnetism as presented in the study materials?

Accepted Answer

Electric and magnetic effects are interconnected; changing magnetic fields produce electric fields and vice versa.

Question 2

A vector $\vec{A}$ is given by $\vec{A} = 2\hat{i} + 2\hat{j}$ and another vector $\vec{B} = 4\hat{i} - \hat{j}$. What is the sum $\vec{C} = \vec{A} + \vec{B}$?

Accepted Answer

$\vec{C} = 6\hat{i} + \hat{j}$

Question 3

Which of the following is true about the dot product of two vectors $\vec{A}$ and $\vec{B}$?

Accepted Answer

The dot product $\vec{A} \cdot \vec{B}$ is a scalar representing the projection of one vector onto another.

Question 4

According to Coulomb’s Law, what is the magnitude of the force between two point charges $q_1$ and $q_2$ separated by a distance $r$?

Accepted Answer

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

Question 5

Which of the following materials is classified as a conductor according to the study materials?

Accepted Answer

Iron

Question 6

A hydrogen atom consists of a single electron and a single proton. If the electron is $r = 10^{-10}$ m from the proton, what is the magnitude of the electrostatic force between them? (Use $k = 9 	imes 10^9$ N·m$^2$/C$^2$, $e = 1.6 	imes 10^{-19}$ C)

Accepted Answer

$F = 2.3 	imes 10^{-8}$ N

Question 7

Which statement about electric charge is correct?

Accepted Answer

Electric charge is a basic attribute of matter, like mass, and can be positive, negative, or neutral.

Question 8

If three point charges are placed along a straight line, which principle allows you to calculate the net force on one of the charges?

Accepted Answer

Superposition principle

Question 9

Which of the following is NOT a fundamental force described in the study materials?

Accepted Answer

Frictional force

Question 10

A uniform spherical shell of mass $m$ exerts a gravitational force on a test mass inside the shell. According to the shell theorem, what is the net force on the test mass?

Accepted Answer

The net force is zero.

Question 11

Which equation represents the cross product of two vectors $\vec{A}$ and $\vec{B}$?

Accepted Answer

$\vec{A} 	imes \vec{B} = (A_x B_y - A_y B_x) \hat{k}$

Question 12

Which of the following best describes the behavior of charges in a conductor?

Accepted Answer

Electrons move easily from atom to atom, allowing electricity to pass through.

Question 13

In a real-world scenario, why is it important for power plants to use conductors in their transmission lines?

Accepted Answer

Conductors allow efficient transmission of electricity over long distances with minimal energy loss.

Question 14

If a charge $+Q$ is placed between two negative charges $-q$ and $-2q$ separated by a distance $L$, at what position $y$ (measured from $-q$) will the forces on $+Q$ balance?

Accepted Answer

$y = 0.412L$

Question 15

Which of the following is a real-world application of the cross product of vectors?

Accepted Answer

Calculating the torque produced by a force applied at a distance from a pivot point.

Question 16

Which property of insulators allows them to be polarized when a nearby charge is present?

Accepted Answer

Electrons are bound but can be slightly displaced within atoms, causing charge separation.

Question 17

Which of the following is an example of a scalar field?

Accepted Answer

Temperature at every point in a room.

Question 18

What is the main difference between a scalar field and a vector field?

Accepted Answer

A scalar field assigns a magnitude to every point in space, while a vector field assigns both magnitude and direction.

PHYS 121: Electricity and Magnetism – Introduction, Vectors, and Electric Charge

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