Home / AP Physics C E&M – 12.2 Forces on Moving Charges in Magnetic Fields- Exam Style questions- MCQs
An electron is traveling with speed \(v\) when it enters a uniform magnetic field that is directed into the page, as shown above. Five paths in the magnetic field are labeled A, B, C, D, and E.
Which labeled path best shows the path the electron will follow as it travels through the magnetic field?
Correct Answer: \( \boxed{\mathrm{D}} \)
The magnetic force on a moving charged particle is given by the Lorentz force equation:
\( \vec{F}=q\vec{v}\times\vec{B} \)
The electron enters the magnetic field moving to the right, while the magnetic field points into the page.
Using the right-hand rule for a positive charge, \( \vec{v}\times\vec{B} \) points upward. Since an electron has negative charge, the magnetic force is in the opposite direction, which is downward.
The magnetic force is always perpendicular to the velocity, so it changes only the direction of motion and not the speed. Therefore, the electron follows a curved (circular) path rather than a straight line.
The radius of the circular path is given by
\( r=\dfrac{mv}{|q|B} \)
Since the force is directed downward immediately after entering the field, the correct trajectory is the downward-curving path labeled D.
Therefore, the correct answer is (D).
Three long wires perpendicular to the page are equidistant from each other, as shown in the cross-sectional view above. Two wires carry current into the page, and the third carries current out of the page. All the currents are equal in magnitude. What is the direction of the net magnetic force on wire \(A\) due to the other two wires?
Correct Answer: \( \boxed{\mathrm{E}} \)
The magnetic force between two parallel current-carrying wires is
\( \dfrac{F}{L}=\dfrac{\mu_0I_1I_2}{2\pi r} \)
Currents in the same direction attract, while currents in opposite directions repel.
Wire \(A\) carries current into the page.
Because the two wires are equidistant from wire \(A\) and carry equal currents, the two forces have equal magnitudes. Their vertical components cancel, while their horizontal components both point to the right.
Therefore, the net magnetic force on wire \(A\) is toward the right.
Hence, the correct answer is (E).
A uniform magnetic field points into the page. Three subatomic particles are shot into the field from the left-hand side of the page. All have the same initial speed and direction. These particles take paths A, B, and C, as labeled in the diagram above.
Which of the following is a possible identity for each particle?
Correct Answer: \( \boxed{\mathrm{E}} \)
The magnetic force on a charged particle is
\( \vec{F}=q\vec{v}\times\vec{B} \).
Since the magnetic field points into the page and all particles initially move to the right:
• A positive charge is deflected upward.
• A negative charge is deflected downward.
• A neutral particle experiences no magnetic force and continues straight.
Therefore:
• Particle A, which curves downward, must be an electron.
• Particle B, which curves upward, must be a proton.
• Particle C, which continues in a straight line, must be a neutron.
The tighter curvature of the electron is consistent with its much smaller mass. The radius of curvature is
\( r=\dfrac{mv}{|q|B} \),
so the lighter electron has a much smaller radius than the proton.
Therefore, the correct answer is (E).