AP Physics C E and M 12.2: Force on Moving Charges

Describe the force exerted on a moving charged object by a magnetic field and relate its direction and magnitude to velocity and field orientation.

[Maximum number: 5]

Long, parallel wires S and T are a distance 2 d apart. Both wires carry equal currents I, but the

currents are in opposite directions. Both wires are parallel to the x-axis. At the instant shown

in Figure 1, Sphere 1 is a distance d above Wire S, Sphere 2 is a distance d below Wire S, and

both spheres are moving with speed v in the +x-direction. Each sphere has positive charge +Q.

Gravitational effects are negligible.

Figure 1

(a)

$F_{1}$ is the magnitude of the magnetic force exerted on Sphere 1 due to the currents in wires S

and T. $F_{2}$ is the magnitude of the magnetic force exerted on Sphere 2 due to the currents in

wires S and T.

Indicate whether $F_{2}$ is greater than, less than, or equal to $F_{1}$ by writing one of the following.

- $F_{2}>F_{1}$

- $F_{2}<F_{1}$

- $F_{2}=F_{1}$

Justify your answer.

[ 3 ]

\multirow[t]{4}{*}{A} & For indicating that $F_{2}>F_{1}$ & Point A1 \\ \hline & For correctly relating the magnitude of the magnetic force to the magnitude of the magnetic field & Point A2 \\ \hline & For indicating that the magnitude of the magnetic field at the location of Sphere 2 is greater than the magnitude of the magnetic field at the location of Sphere 1 by referring to either: - The direction of the magnetic fields from Wires S and T at the locations of the spheres & Point A3 \\ \hline &

Example Response
The magnitude of the magnetic force exerted on a sphere is directly proportional to Q, v, and B. Because Q and v are the same for both spheres, the difference in the magnitudes of the magnetic forces is due to the difference in the magnitudes of the magnetic fields at the locations of the spheres. The magnitude of the magnetic field is greater at the location of Sphere 2 than at the location of Sphere 1 because the fields from the wires are in the same direction. Therefore, $F_{2}>F_{1}$ .

Example Response

The magnitude of the magnetic force exerted on a sphere is directly proportional to Q, v, and B. Because Q and v are the same for both spheres, the difference in the magnitudes of the magnetic forces is due to the difference in the magnitudes of the magnetic fields at the locations of the spheres. The magnitude of the magnetic field is greater at the location of Sphere 2 than at the location of Sphere 1 because the fields from the wires are in the same direction. Therefore,

F_{2}>F_{1}

.

& \\ \hline

(b)

Later, Wire T carries current 3 I in the +x-direction. At the instant shown in Figure 2,

Sphere 2 is a distance d below Wire S and is moving with speed v in the +x-direction. $F_{\text {new }}$ is

the new magnitude of the magnetic force exerted on Sphere 2 due to the currents in wires S

and T.

Figure 2

Indicate whether $F_{\text {new }}$ is greater than, less than, or equal to $F_{2}$ by writing one of the

following.

- $F_{\text {new }}>F_{2}$

- $F_{\text {new }}<F_{2}$

- $F_{\text {new }}=F_{2}$

Briefly justify your answer by referencing your derivation in part B.

[ 2 ]

\multirow[t]{3}{*}{C} & For indicating $F_{\text {new }}=F_{2}$ & Point C1 \\ \hline &

For indicating $B_{\text {tot }}=\frac{3 \mu_{0} I}{2 \pi d}-\frac{\mu_{0} I}{2 \pi d}$
OR
For indicating that the net magnitude of the magnetic field at the location of Sphere 2 will remain the same even though the field from Wire T will change

& Point C2 \\ \hline &

Example Response
The magnetic field at the location of Sphere 2 due to the current in Wire T is in the opposite direction to the magnetic field due to the current in Wire S. The current in Wire T is increased by a factor of 3. Therefore, $B_{\text {tot }}=\frac{3 \mu_{0} I}{2 \pi d}-\frac{\mu_{0} I}{2 \pi d}=\frac{\mu_{0} I}{\pi d}$ in this scenario. Thus, $F_{\text {new }}=F_{2}$ .

& \\ \hline \end{tabular}

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12.2.B—Describe the force exerted on moving charged objects by a magnetic field question 1

Question (a)

Question (b)