Q: If the electric field $$\vec{E}$$ makes an angle $$\theta$$ with the normal to a surface element $$dA$$, what is the contribution to the electric flux from this element?

$$\displaystyle E \ dA \cos\theta$$

Question 1

Which of the following best describes the physical meaning of the electric flux $$\Phi_E$$ through a closed surface?

Accepted Answer

It is the total number of electric field lines crossing the surface, proportional to the net charge enclosed.

Question 2

According to Gauss's Law, what is the mathematical relationship between the electric flux through a closed surface and the charge enclosed?

Accepted Answer

$$\displaystyle \oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\$$varepsilon_0$$}$$

Question 3

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

Accepted Answer

$$\displaystyle \frac{q}{\$$varepsilon_0$$}$$

Question 4

Which of the following statements about Gauss's Law is correct?

Accepted Answer

The size of the Gaussian surface does not affect the total electric flux; only the net charge enclosed matters.

Question 5

A cube encloses a point charge $$q at $$its center. What is the electric flux through one face of the cube?

Accepted Answer

$$\displaystyle \frac{q}{6\$$varepsilon_0$$}$$

Question 6

If the electric field $$\vec{E}$$ makes an angle $$	heta$$ with the normal to a surface element $$dA$$, what is the contribution to the electric flux from this element?

Accepted Answer

$$\displaystyle E \ dA \cos	heta$$

Question 7

A closed surface contains no net charge inside. What is the total electric flux through the surface?

Accepted Answer

Zero, because $$Q_{enc} = 0 so$$ $$\Phi_E = 0.$$

Question 8

Which of the following is a necessary step when using Gauss's Law to solve for the electric field $$\vec{E}$$?

Accepted Answer

Choose a Gaussian surface that matches the symmetry of the charge distribution.

Question 9

A long, straight line of charge has a uniform linear charge density $$\lambda. $$What is the electric field at a distance $$r$$ from the line using Gauss's Law?

Accepted Answer

$$\displaystyle \frac{\lambda}{2\pi \$$varepsilon_0$$ r}$$

Question 10

Which of the following best explains why the electric flux through a closed surface is proportional to the net charge enclosed and not to the total charge on the surface?

Accepted Answer

Only charges inside the surface contribute to the net number of field lines crossing the surface; charges on the surface do not contribute to net flux.

Question 11

A non-uniform electric field passes through a flat surface. Which expression gives the total electric flux through the surface?

Accepted Answer

$$\displaystyle \int \vec{E} \cdot d\vec{A}$$

Question 12

If the electric field is parallel to the surface at every point, what is the electric flux through the surface?

Accepted Answer

Zero, because $$\cos 90^\circ = 0$$ and $$\vec{E} \cdot d\vec{A} = 0.$$

Question 13

A closed surface encloses two charges: $$+2\mu C$$ and $$-2\mu C. $$What is the net electric flux through the surface?

Accepted Answer

Zero, because the net enclosed charge is zero.

Question 14

Which of the following is NOT a valid application of Gauss's Law?

Accepted Answer

Calculating the electric field at a point outside a non-symmetric charge distribution.

Question 15

A spherical shell of radius $$R$$ carries a uniform charge $$Q$$ distributed on its surface. What is the electric field at a point inside the shell ($$r \u003c R$$)?

Accepted Answer

Zero, because no charge is enclosed by a Gaussian surface inside the shell.

Question 16

A flat surface of area $$A is $$placed in a uniform electric field $$E. $$The field makes an angle $$	heta$$ with the normal to the surface. What is the total electric flux through the surface?

Accepted Answer

$$\displaystyle EA \cos	heta$$

Question 17

Which of the following best describes the role of the normal vector $$\hat{n} in $$calculating electric flux?

Accepted Answer

It defines the direction perpendicular to the surface, used in the dot product $$\vec{E} \cdot d\vec{A}.$$

Question 18

A closed surface in a region of space contains a uniform electric field but no charges. What is the net electric flux through the surface?

Accepted Answer

Zero, because there is no net charge enclosed.

Question 19

Which of the following is a correct step in applying Gauss's Law to find the electric field of a charged object?

Accepted Answer

Choose a Gaussian surface where the electric field is either constant or zero everywhere on the surface.

Gauss's Law and Electric Flux: Study Notes for College Physics

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