Q: A satellite is orbiting close to the Earth's surface. What is the approximate acceleration due to gravity it experiences?

$$a_g = G \frac{M_{\text{Earth}}}{r^2$} \approx g$$

Q: A spacecraft needs to escape Earth's gravity. What is the correct formula for the escape velocity from the surface of a planet of mass $$M$$ and radius $$R$$?

$$v_{\text{esc}} = \sqrt{\frac{2GM}{R}}$$

Q: A dipole with dipole moment $$\vec{p} is $$placed in a uniform electric field $$\vec{E}. $$What is the torque $$\vec{\tau}$$ experienced by the dipole?

$$\vec{\tau} = \vec{p} \times \vec{E}$$

Question 1

Which of the following correctly expresses Newton's law of universal gravitation for the force between two point masses $$m_1$$ and $$m_2$$ separated by a distance $$r$$?

Accepted Answer

$$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 2

According to Shell Theorem 1, what is the gravitational force experienced by a mass located outside a uniform spherical shell of mass $$M$$?

Accepted Answer

It is as if all the mass $$M$$ were concentrated at the center of the shell.

Question 3

A satellite is orbiting close to the Earth's surface. What is the approximate acceleration due to gravity it experiences?

Accepted Answer

$$a_g = G \frac{M_{	ext{Earth}}}{r^2$} \approx g$$

Question 4

Which of the following statements about gravitational potential energy $$U$$ between two masses $$m_1$$ and $$m_2$$ separated by distance $$r is $$correct?

Accepted Answer

$$U = -G \frac{m_1$ m_2$}{r}$$

Question 5

A spacecraft needs to escape Earth's gravity. What is the correct formula for the escape velocity from the surface of a planet of mass $$M$$ and radius $$R$$?

Accepted Answer

$$v_{	ext{esc}} = \sqrt{\frac{2GM}{R}}$$

Question 6

Which of the following best describes the work done by a force $$\vec{F}$$ along a path $$d\vec{r}$$?

Accepted Answer

$$W = \int \vec{F} \cdot d\vec{r}$$

Question 7

Which of the following is a correct statement about the conservation of energy in an isolated system?

Accepted Answer

$$U_f + K_f = U_i + K_i$$

Question 8

Coulomb’s law describes the force between two point charges $$q_1$$ and $$q_2$$ separated by a distance $$r. $$Which is the correct formula?

Accepted Answer

$$F = k \frac{q_1$ q_2$}{r^2$}$$

Question 9

Which of the following statements about electric charge is correct?

Accepted Answer

Electric charge is conserved and quantized.

Question 10

A point charge $$q$$ creates an electric field at a distance $$r. $$What is the correct expression for the electric field $$\vec{E}$$?

Accepted Answer

$$\vec{E} = k \frac{q}{r^2$} \hat{r}$$

Question 11

Which of the following best describes the electric field produced by a very long straight wire with linear charge density $$\lambda at a $$distance $$r$$ from the wire?

Accepted Answer

$$E = \frac{\lambda}{2 \pi \$$epsilon_0$$ r}$$

Question 12

A dipole with dipole moment $$\vec{p} is $$placed in a uniform electric field $$\vec{E}. $$What is the torque $$\vec{	au}$$ experienced by the dipole?

Accepted Answer

$$\vec{	au} = \vec{p} 	imes \vec{E}$$

Question 13

Which of the following is the correct mathematical statement of Gauss’s law?

Accepted Answer

$$\Phi = \oint \vec{E} \cdot d\vec{A} = \frac{q_{	ext{encl}}}{\$$epsilon_0$$}$$

Question 14

A solid conducting sphere carries a net charge. According to Gauss’s law, what is the electric field inside the conductor?

Accepted Answer

Zero everywhere inside the conductor.

Question 15

Which of the following is true about the electric field just outside the surface of a charged conductor in electrostatic equilibrium?

Accepted Answer

It is perpendicular to the surface and proportional to the surface charge density.

Question 16

A charged spherical shell of radius $$R$$ carries a total charge $$Q. $$What is the electric field at a point inside the shell ($$r \u003c R$$)?

Accepted Answer

Zero everywhere inside the shell.

Question 17

A large, flat, infinite plane of charge has a uniform surface charge density $$\sigma. $$What is the electric field just above the surface?

Accepted Answer

$$E = \frac{\sigma}{2 \$$epsilon_0$$}$$

Question 18

Which of the following best describes the superposition principle for forces?

Accepted Answer

The net force is the vector sum of all individual forces.

Question 19

A point charge $$q is $$placed at the center of a spherical Gaussian surface of radius $$r. $$What is the total electric flux through the surface?

Accepted Answer

$$\Phi = \frac{q}{\$$epsilon_0$$}$$

Question 20

A charged rod creates an electric field with cylindrical symmetry. Which method is most appropriate to calculate the field at a distance $$r$$ from the rod?

Accepted Answer

Apply Gauss’s law using a cylindrical Gaussian surface.

Midterm 1 Physics Study Guide: Gravitation, Coulomb's Law, Electric Field, and Gauss's Law

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