Q: A charged particle moves in a region with both electric and magnetic fields. Which equation gives the force on the particle?

$$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$$

Question 1

A long solenoid has $$n$$ loops per unit length and carries a current $$I. $$Using Ampère's law, what is the magnitude of the magnetic field inside the solenoid?

Accepted Answer

$$B = \mu_0$ n I$$

Question 2

What is the direction of the magnetic field inside a solenoid relative to the current direction?

Accepted Answer

Parallel to the axis of the solenoid, following the right-hand rule

Question 3

According to Ampère's law, what is the magnetic field outside a long solenoid?

Accepted Answer

It is zero

Question 4

A uniformly charged sphere of radius $$R$$ has total charge $$Q. $$What is the electric field at a distance $$r$$ from the center, where $$r \u003e R$$?

Accepted Answer

$$E = \frac{Q}{4\pi \$$epsilon_0$$ r^2$}$$

Question 5

For a uniformly charged sphere, what is the electric field at a distance $$r$$ from the center, where $$r \u003c R$$?

Accepted Answer

$$E = \frac{Q r}{4\pi \$$epsilon_0$$ R^3$}$$

Question 6

In an RLC circuit powered by an alternating source, the voltage across the inductor is given by $$V_L(t). $$Which expression correctly represents $$V_L(t)$$?

Accepted Answer

$$V_L(t) = L \frac{dI}{dt}$$

Question 7

For an RLC circuit, the impedance $$Z is $$minimized at the resonant frequency. Which equation gives the resonant angular frequency $$\$$omega_0$$?

Accepted Answer

$$\$$omega_0$$ = \frac{1}{\sqrt{LC}}$$

Question 8

Given $$V_{max} = 160\,	ext{V}$$, $$R = 100\,\Omega$$, $$C = 3.0\,\mu	ext{F}$$, and $$L = 1.0\,	ext{mH}$$, what is the maximum current $$I_{max} at $$resonance in the RLC circuit?

Accepted Answer

$$I_{max} = \frac{V_{max}}{R}$$

Question 9

In an RLC circuit, what is the phase relationship between the voltage across the capacitor and the current?

Accepted Answer

Voltage lags current by $$90^\circ$$

Question 10

A current-carrying wire produces a magnetic field. Which rule is used to determine the direction of the magnetic field around the wire?

Accepted Answer

Right-hand rule

Question 11

A laser emits an oscillating electric field. What is the effect on the magnetic field in the region?

Accepted Answer

The magnetic field oscillates perpendicular to the electric field

Question 12

Which law is used to calculate the electric field due to a uniformly charged sphere?

Accepted Answer

Gauss's law

Question 13

In an RLC circuit, what happens to the impedance $$Z as $$the frequency increases far above the resonant frequency?

Accepted Answer

Impedance increases due to the inductor

Question 14

A wire carries a current $$I in $$the $$+x$$ direction. Using the right-hand rule, what is the direction of the magnetic field at a point above the wire?

Accepted Answer

Into the page

Question 15

Which equation correctly expresses Faraday's law of electromagnetic induction?

Accepted Answer

$$\mathcal{E} = -\frac{d\Phi_B}{dt}$$

Question 16

A charged particle moves in a region with both electric and magnetic fields. Which equation gives the force on the particle?

Accepted Answer

$$\vec{F} = q(\vec{E} + \vec{v} 	imes \vec{B})$$

Question 17

In a solenoid, if the current is doubled, what happens to the magnetic field inside?

Accepted Answer

It doubles

Question 18

Which of the following best describes the phasor diagram for an RLC circuit at resonance?

Accepted Answer

Voltage across inductor and capacitor cancel, leaving only resistor voltage

Question 19

A magnetic field is changing in time. According to Faraday's law, what is induced in a nearby loop?

Accepted Answer

An electromotive force (emf)

Question 20

In a real-world scenario, a medical MRI machine uses a strong solenoid. Why is the field inside the solenoid nearly uniform?

Accepted Answer

Because the field outside is zero and inside is constant due to symmetry

Physics Final Exam Study Guidance: Solenoids, Gauss' Law, and RLC Circuits

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