Electricity and Magnetism Practice

Two point charges, $q_1 = +3\,\mu\text{C}$ and $q_2 = -2\,\mu\text{C}$, are separated by $0.50\ \text{m}$.

Find the magnitude of the force between them and state whether the force is attractive or repulsive.

A charge of $+5.0\ \text{nC}$ is located in space.

What is the magnitude of the electric field $0.20\ \text{m}$ away from the charge, and what is its direction?

A uniform charge of $12\ \mu\text{C}$ is spread along a thin wire of length $3.0\ \text{m}$.

What is the linear charge density $\lambda$?

A uniform electric field of magnitude $200\ \text{N/C}$ passes through a flat surface of area $0.15\ \text{m}^2$.

The angle between the field and the surface normal is $30^\circ$.

What is the electric flux?

A closed surface has electric flux

What charge is enclosed by the surface?

At a point in space, a $+4.0\ \text{nC}$ charge is $0.30\ \text{m}$ away and a $-1.0\ \text{nC}$ charge is $0.20\ \text{m}$ away.

What is the electric potential at that point?

A charge of $+3.0\ \mu\text{C}$ moves from a point at $20\ \text{V}$ to a point at $-10\ \text{V}$.

What is the change in its electric potential energy?

A capacitor has capacitance $2.0\ \mu\text{F}$ in vacuum. After a dielectric is inserted, its capacitance becomes $6.0\ \mu\text{F}$.

What is the dielectric constant $\kappa$?

A wire has resistivity $2.0\times 10^{-6}\ \Omega\cdot\text{m}$, length $4.0\ \text{m}$, and cross-sectional area $2.0\times 10^{-6}\ \text{m}^2$.

Find its resistance, and then find the current if a $12\ \text{V}$ potential difference is applied across it.

A straight wire segment of length $0.30\ \text{m}$ carries a current of $5.0\ \text{A}$. It is placed in a uniform magnetic field of magnitude $0.40\ \text{T}$, and the wire is perpendicular to the field.

What is the magnitude of the magnetic force on the wire?

Two charges lie on a line: a $+6.0\ \text{nC}$ charge on the left and a $-6.0\ \text{nC}$ charge on the right. A point is exactly halfway between them, $0.10\ \text{m}$ from each charge.

What is the net electric field at the midpoint?

An infinite sheet of charge has surface charge density

What is the electric field magnitude on either side of the sheet, and what is the direction?

A $3.0\ \mu\text{C}$ charge moves from a point at $20\ \text{V}$ to a point at $-10\ \text{V}$.

How much work does the electric field do on the charge?

Two capacitors of $3.0\ \mu\text{F}$ and $6.0\ \mu\text{F}$ are connected in series across a $12\ \text{V}$ battery.

Find the equivalent capacitance and the charge on each capacitor.

A $12\ \text{V}$ battery is connected in series with a $2\ \Omega$ resistor and a $4\ \Omega$ resistor.

Find the circuit current and the power dissipated by the $4\ \Omega$ resistor.

An RC circuit has $R = 2.0\ \text{k}\Omega$, $C = 100\ \mu\text{F}$, and is connected to a $12\ \text{V}$ battery.

Find the time constant and the charge on the capacitor after one time constant has passed.

A long straight wire carries a current of $8.0\ \text{A}$.

What is the magnetic field magnitude $5.0\ \text{cm}$ from the wire?

A proton moves perpendicular to a uniform magnetic field of magnitude $0.50\ \text{T}$ with speed $2.0\times 10^5\ \text{m/s}$.

What is the radius of its circular path?

An infinite line of charge has linear charge density

What is the electric field magnitude $0.20\ \text{m}$ from the line?

A solenoid has $900$ turns over a length of $0.30\ \text{m}$ and carries a current of $2.0\ \text{A}$.

What is the magnetic field inside the solenoid?

A circular loop lies in the page. The magnetic field through the loop points into the page and is increasing.

What is the direction of the induced current?

A metal bar of length $0.40\ \text{m}$ slides at $5.0\ \text{m/s}$ through a magnetic field of magnitude $0.80\ \text{T}$. The bar and its motion are perpendicular to the field. The circuit resistance is $2.0\ \Omega$.

Find the induced emf and the current in the circuit.

An RL circuit has resistance $4.0\ \Omega$, inductance $0.20\ \text{H}$, and final current $3.0\ \text{A}$.

What is the time constant, and what is the current after $0.05\ \text{s}$?

A capacitor is charging in a circuit, and the conduction current in the wire is $0.40\ \text{A}$.

According to Maxwell's equations, what must the displacement current term between the capacitor plates be, and why?

Two charges, $+2.0\ \text{nC}$ and $-2.0\ \text{nC}$, are placed on a line, each $0.10\ \text{m}$ from the midpoint.

What are the electric potential and the electric field at the midpoint?

A closed surface encloses a net charge of $+3.0\ \text{nC}$ and also surrounds a bar magnet.

What are the net electric flux and the net magnetic flux through the surface?

A circular loop lies in the page. The magnetic field through the loop points out of the page and is increasing.

Take counterclockwise circulation as the positive loop direction.

What is the sign of the induced emf, and what is the actual current direction?