Question 1

Which of the following statements best describes the electric field $$\vec{E}$$?

Accepted Answer

It is the region of space affected by the action of electric charge.

Question 2

What is the mathematical expression for the magnitude of the electric field $$\vec{E}$$ due to a point charge $$Q at a $$distance $$r$$?

Accepted Answer

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

Question 3

Which property is NOT true about electric field lines?

Accepted Answer

Electric field lines can form closed loops.

Question 4

A thin rod of length $$L$$ carries a total charge $$Q$$ distributed uniformly along its length. What is the linear charge density $$\lambda$$?

Accepted Answer

$$\lambda = \frac{Q}{L}$$

Question 5

If the electric field at a point is $$\vec{E}$$ and a charge $$q_0 is $$placed at that point, what is the force $$\vec{F}_0$$ experienced by the charge?

Accepted Answer

$$\vec{F}_0 = q_0$ \vec{E}$$

Question 6

Which of the following is the correct expression for the electric flux $$\Phi$$ through a surface $$A$$ when the electric field $$\vec{F}$$ makes an angle $$	heta$$ with the normal to the surface?

Accepted Answer

$$\Phi = F A \cos 	heta$$

Question 7

What is the value of the constant $$k in $$Coulomb's law in terms of the permittivity of free space $$\$$varepsilon_0$$?

Accepted Answer

$$k = \frac{1}{4 \pi \$$varepsilon_0$$}$$

Question 8

A positive test charge is placed in an electric field created by a negative point charge. In which direction does the force on the test charge point?

Accepted Answer

Toward the negative charge

Question 9

Which of the following best describes the relationship between the strength of the electric field and the distance from a point charge?

Accepted Answer

The electric field decreases as $$1/r^2$$ with distance.

Question 10

Which of the following is a necessary condition for the validity of Coulomb's law?

Accepted Answer

The charges must have a spherically symmetric distribution.

Question 11

What is the electric field at a point $$P$$ located $$1\,\mathrm{m}$$ from the right end of a $$2\,\mathrm{m}$$ rod carrying a total charge of $$98\,\mu\mathrm{C}$$ distributed uniformly along its length?

Accepted Answer

$$E = \frac{1}{4 \pi \$$varepsilon_0$$} \int_{0}^{2} \frac{\lambda}{x^2$} dx$$ where $$\lambda = \frac{98 	imes 10$$^{-6}$$}{2}$$

Question 12

Which of the following is the correct integral expression for the electric field due to a continuous linear distribution of charge?

Accepted Answer

$$E = \frac{1}{4 \pi \$$varepsilon_0$$} \int \frac{\lambda}{r^2$} dl$$

Question 13

Which of the following statements about divergence is correct?

Accepted Answer

Divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.

Question 14

According to Gauss' law, the total electric flux $$\Phi_E$$ through a closed surface enclosing a charge $$Q is $$given by:

Accepted Answer

$$\Phi_E = \frac{Q}{\$$varepsilon_0$$}$$

Question 15

If the electric field $$\vec{E} is $$perpendicular to a surface of area $$A$$, what is the electric flux through the surface?

Accepted Answer

$$\Phi = E A$$

Question 16

Which of the following is true about the direction of electric field lines for a positive and a negative point charge?

Accepted Answer

Electric field lines point away from positive charges and toward negative charges.

Question 17

A surface is oriented at an angle $$	heta to a $$uniform electric field $$\vec{E}. $$Which orientation gives the maximum electric flux through the surface?

Accepted Answer

$$	heta = 0^\circ$$

Question 18

Which of the following is the correct vector form for the electric flux $$\Phi$$ through a surface?

Accepted Answer

$$\Phi = \int \vec{F} \cdot d\vec{A}$$

Electric Field and Gauss' Law: Study Notes for Calculus-Based Physics

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