AP® Physics C: E&M - Magnetic Fields - MCQs
Question
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?
(A) Path A
(B) Path B
(C) Path C
(D) Path D
(E) Path E
Answer/Explanation
Ans:D Using the right-hand rule for the magnetic force (from the Lorentz force equation), \(\vec{F}=\vec{qv}\times \vec{B}\) the direction of velocity to the right crossed with the magnetic field perpendicular and into the page results in a magnetic force acting on the moving charge up toward the top of the page. However, since the charge is negative, the direction of the magnetic force acts down on the electron. Since force is being applied to the electron as soon as it enters the B field, it begins accelerating due the relationship \(\vec{F}=m\vec{a}\) Since the electron
is accelerating, the path that the electron deflects down is not linear
but a curve, as shown by path D.
Question
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.
The electron is replaced with a proton that is traveling at the same speed v in the same direction as it enters the magnetic field. Which of the following best describes the motion of the proton as it passes through the magnetic field?
I. The speed of the proton changes less than the speed of the electron did.
II. The proton is deflected in the opposite direction.
III. The proton is deflected more than the electron.
(A) I only
(B) I and II only
(C) II only
(D) II and III only
(E) I, II and III
Answer/Explanation
Ans:C If the electron is replaced with a positive charge, the resulting force due to the magnetic field, the magnetic force, will act in the positive direction, or upward. This can be determined using the correct right-hand rule for the Lorentz force equation, \(\vec{F}=q\vec{v}\times \vec{B}\). Since a force is acting on the charge, it is accelerating up as well. Also, since the mass of an electron is much smaller than the mass of a proton, then \(M_electron \)<\(m_proton\). Since a= \frac{F}{m}\)then \(a_electron> a _proton\); thus, the proton would deflect less than an electron.
Question
Which of the following is NOT equal to one tesla?
(A) 1 J/(A•m2 )
(B) 1 kg/(C•s)
(C) 1 N/(A•m)
(D) 1 V•s/m2
(E) lA•N/V
Answer/Explanation
Ans: E
From the equation F = qvB, we see that 1 tesla is equal to 1 N·s/(C·m). Since
\(\frac{1N.s}{C.m}=\frac{1N}{A.m}=\frac{1J}{A.m^{2}}\)
(A) and (C) are eliminated.
Furthermore,
\(\frac{1N.s}{C.m}=\frac{1kg.m/s}{C.m}=\frac{1kg}{C.s}\)
eliminating (B). Finally, since
\(\frac{1J}{A.m^{2}}=\frac{1C.V}{C/s.m^{2}}=\frac{1V.s}{m^{2}}\)
(D) is also eliminated.