Q: Which of the following equations correctly expresses Gauss's Law for the electric field in integral form?

$$\displaystyle \int \vec{E} \cdot d\vec{A} = \frac{Q_{\text{encl}}}{\$$varepsilon_0$$}$$

Q: A proton is accelerated from rest through a potential difference of $$1.0\ \text{MV}. $$What is its final kinetic energy?

$$\displaystyle 1.0\ \text{MeV}$$

Q: A transformer has a primary coil with 100 turns and a secondary coil with 500 turns. If the input voltage is $$120\ \text{V}$$, what is the output voltage (assuming 100% efficiency)?

$$\displaystyle 600\ \text{V}$$

Q: A particle with charge $$q$$ and velocity $$v$$ enters a magnetic field $$B at an $$angle $$\theta to $$the field. What is the magnitude of the magnetic force on the particle?

$$\displaystyle F = q v B \sin \theta$$

Q: A capacitor of $$10\ \mu\text{F} is $$charged to $$100\ \text{V}$$ and then disconnected from the battery. What is the energy stored in the capacitor?

$$\displaystyle U = \frac{1}{2} C V^2$ = 0.05\ \text{J}$$

Q: A monochromatic light of wavelength $$500\ \text{nm}$$ passes through a single slit of width $$2.0\ \mu\text{m}. At $$what angle does the first minimum occur?

$$\displaystyle \theta = \arcsin\left(\frac{\lambda}{a}\right) = \arcsin\left(\frac{500 \times 10$$^{-9}$$}{2.0 \times 10$$^{-6}$$}\right) \approx 14.5^\circ$$

Question 1

Which of the following equations correctly expresses Gauss's Law for the electric field in integral form?

Accepted Answer

$$\displaystyle \int \vec{E} \cdot d\vec{A} = \frac{Q_{	ext{encl}}}{\$$varepsilon_0$$}$$

Question 2

A parallel-plate capacitor is filled with a dielectric material of dielectric constant $$\kappa. If $$the original capacitance without the dielectric is $$C_0$$, what is the new capacitance?

Accepted Answer

$$\displaystyle C = \kappa C_0$

Question 3

A proton is accelerated from rest through a potential difference of $$1.0\ 	ext{MV}. $$What is its final kinetic energy?

Accepted Answer

$$\displaystyle 1.0\ 	ext{MeV}$$

Question 4

Which of the following correctly gives the energy stored in an inductor with current $$I$$ and inductance $$L$$?

Accepted Answer

$$\displaystyle U = \frac{1}{2} L I^2$

Question 5

A wire of length $$L$$ carries a current $$I in a $$uniform magnetic field $$B$$ perpendicular to the wire. What is the magnitude of the force on the wire?

Accepted Answer

$$\displaystyle F = B I L$$

Question 6

A transformer has a primary coil with 100 turns and a secondary coil with 500 turns. If the input voltage is $$120\ 	ext{V}$$, what is the output voltage (assuming 100% efficiency)?

Accepted Answer

$$\displaystyle 600\ 	ext{V}$$

Question 7

Which equation gives the resonant angular frequency $$\$$omega_0$$ for an LC circuit?

Accepted Answer

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

Question 8

A light ray passes from air ($$n=1.00) $$into glass ($$n=1.50) at an $$angle of $$30^\circ to $$the normal. What is the angle of refraction in the glass?

Accepted Answer

$$\displaystyle 19.5^\circ$$

Question 9

Which of the following is the correct expression for the energy of a photon?

Accepted Answer

$$\displaystyle E = h f$$

Question 10

A particle with charge $$q$$ and velocity $$v$$ enters a magnetic field $$B at an $$angle $$	heta to $$the field. What is the magnitude of the magnetic force on the particle?

Accepted Answer

$$\displaystyle F = q v B \sin 	heta$$

Question 11

A capacitor of $$10\ \mu	ext{F} is $$charged to $$100\ 	ext{V}$$ and then disconnected from the battery. What is the energy stored in the capacitor?

Accepted Answer

$$\displaystyle U = \frac{1}{2} C V^2$ = 0.05\ 	ext{J}$$

Question 12

Which of the following best describes the relationship between the speed of light $$c$$, the permeability of free space $$\mu_0$, and the permittivity of free space $$\$$varepsilon_0$$?

Accepted Answer

$$\displaystyle c = \frac{1}{\sqrt{\mu_0$ \$$varepsilon_0$$}}$$

Question 13

A monochromatic light of wavelength $$500\ 	ext{nm}$$ passes through a single slit of width $$2.0\ \mu	ext{m}. At $$what angle does the first minimum occur?

Accepted Answer

$$\displaystyle 	heta = \arcsin\left(\frac{\lambda}{a}ight) = \arcsin\left(\frac{500 	imes 10$$^{-9}$$}{2.0 	imes 10$$^{-6}$$}ight) \approx 14.5^\circ$$

Question 14

Which equation gives the relativistic total energy of a particle with rest mass $$m$$ and momentum $$p$$?

Accepted Answer

$$\displaystyle E^2$ = (m c^2$)^2 + (p$$ $$c)^2$

Question 15

A $$60\ 	ext{W}$$ light bulb is powered by a $$120\ 	ext{V}$$ rms AC source. What is the rms current through the bulb?

Accepted Answer

$$\displaystyle I_{	ext{rms}} = \frac{P}{V_{	ext{rms}}} = 0.5\ 	ext{A}$$

Question 16

Which of the following is the correct form of the Heisenberg uncertainty principle for position and momentum?

Accepted Answer

$$\displaystyle \Delta x \Delta p \geq \frac{h}{4\pi}$$

Question 17

A lens has a focal length of $$20\ 	ext{cm}. An $$object is placed $$60\ 	ext{cm}$$ from the lens. Where is the image formed?

Accepted Answer

$$\displaystyle \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \Rightarrow d_i = 30\ 	ext{cm}$$

Question 18

Which equation gives the condition for constructive interference in a double-slit experiment?

Accepted Answer

$$\displaystyle d \sin 	heta = m \lambda$$

Question 19

A $$2.0\ \Omega$$ resistor and a $$4.0\ \Omega$$ resistor are connected in parallel. What is the equivalent resistance?

Accepted Answer

$$\displaystyle R_{	ext{eq}} = \left( \frac{1}{2.0} + \frac{1}{4.0} \$$right)^{-1}$$ = 1.33\ \Omega$$

Key Equations and Constants for Electricity, Magnetism, and Modern Physics

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