AP Physics 2: Algebra-Based Practice Quiz: Electric Charge and Electric Force

Correct Answer: B

The provided content states that opposite charges attract. Since one object is positive and the other is negative, they will exert an attractive electric force on each other.

Correct Answer: C

The content explicitly states: 'The smallest indivisible amount of charge is the elementary charge e (charge of electron or proton).'

Correct Answer: D

According to Coulomb's law, the electrostatic force is inversely proportional to the square of the distance between the charges ($|\vec{F}_{E}| \propto 1/r^2$). If the distance is tripled (multiplied by 3), the force will be divided by 3², which is 9. The new force is F/9.

Correct Answer: C

Coulomb's law states that the force is directly proportional to the product of the charges ($|\vec{F}_{E}| \propto |q_1q_2|$). If q₁ is doubled and q₂ is doubled, the product becomes (2q₁)(2q₂) = 4q₁q₂. Therefore, the new force will be 4 times the original force, or 4F.

Correct Answer: B

Gravity is always attractive between two masses. Since electrons have like (negative) charges, the electrostatic force between them is repulsive. The provided content states that 'the magnitude of the gravitational force is usually much smaller than the magnitude of the electrostatic force.'

Correct Answer: C

The content defines electric permittivity as 'a measurement of the degree to which a material or medium is polarized in the presence of an electric field.'

Correct Answer: C

From Coulomb's law, $|\vec{F}_{E}|=\frac{1}{4\pi\epsilon}\frac{|q_{1}q_{2}|}{r^{2}}$, the force is inversely proportional to the permittivity (ε). If the permittivity is doubled, the force is halved. The new force is F/2.

Correct Answer: B

The provided text states: 'The direction of the electrostatic force depends on the signs of the charges; like charges repel, opposite charges attract.'

Correct Answer: C

The charge at x = +L repels +Q, exerting a force to the left. The charge at x = -L also repels +Q, exerting a force to the right. Since the charges (+q) and distances (L) are identical on both sides, the two forces are equal in magnitude and opposite in direction. Therefore, they cancel each other out, resulting in a net force of zero.

Correct Answer: C

The original force is $F = k \frac{q^2}{r^2}$. The new distance is r/2 and the new charges are q and 2q. The new force $F_{new} = k \frac{q(2q)}{(r/2)^2} = k \frac{2q^2}{r^2/4} = 8 \left(k \frac{q^2}{r^2}\right) = 8F$.

Correct Answer: B

The electric force between two objects is an interaction pair. According to Newton's Third Law, the force that charge A exerts on charge B is equal in magnitude and opposite in direction to the force that B exerts on A. Coulomb's Law, $|\vec{F}_{E}|=k\frac{|q_{1}q_{2}|}{r^{2}}$, gives the magnitude of this mutual force.

Correct Answer: B

The term ε₀ is the electric permittivity of free space (a vacuum). For other materials, a different value of permittivity (ε) is used. Since permittivity is a property of the material/medium, the force depends on the medium between the charges.

Correct Answer: C

A proton (positive) and an electron (negative) have opposite charges, so the electric force is attractive. All objects with mass, including protons and electrons, exert an attractive gravitational force on each other. The provided content states that the magnitude of the gravitational force is usually much smaller than the magnitude of the electrostatic force.

Correct Answer: B

For the net force on the third charge to be zero, the forces from +q and +4q must be equal in magnitude and opposite in direction. This can only happen in the region between the two charges. If the third charge is placed to the left of +q or to the right of +4q, the forces from both charges will be in the same direction. Therefore, the third charge must be placed at a point between 0 and L.

Correct Answer: B

The content states that like charges repel. Two electrons both have a negative charge, so they are like charges and will repel each other.

Correct Answer: C

According to Coulomb's Law, the force is inversely proportional to the permittivity of the medium ($F \propto 1/\epsilon$). If the permittivity is increased by a factor of 5, the force will be reduced by a factor of 5. The new force is 100 N / 5 = 20 N.