Q: Which equation correctly expresses the torque $$\vec{\tau}$$ experienced by an electric dipole in a uniform electric field $$\vec{E}$$?

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

Q: A door is pushed at its edge perpendicular to its surface. Which equation best describes the torque produced about the hinges?

$$\vec{\tau} = \vec{l} \times \vec{F}$$

Q: A disk of radius $$r = 0.10\,\text{m} is $$placed in a uniform electric field $$E = 1.0 \times 10^3$\,\text{N/C} at an $$angle $$30^\circ to $$the field. What is the electric flux through the disk?

$$\Phi_E = 27\,\text{N m}^2/\text{C}$$

Q: Which equation represents Gauss’s Law?

$$\Phi_E = \oint \vec{E} \cdot d\vec{S} = \frac{Q_{\text{enclosed}}}{\$$epsilon_0$$}$$

Question 1

Which equation correctly expresses the torque $$\vec{	au}$$ experienced by an electric dipole in a uniform electric field $$\vec{E}$$?

Accepted Answer

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

Question 2

A door is pushed at its edge perpendicular to its surface. Which equation best describes the torque produced about the hinges?

Accepted Answer

$$\vec{	au} = \vec{l} 	imes \vec{F}$$

Question 3

Which rule is used to determine the direction of the cross product $$\vec{A} 	imes \vec{B} in $$vector operations?

Accepted Answer

Right hand rule

Question 4

If an electric dipole is placed in a uniform electric field, what is the net force acting on the dipole?

Accepted Answer

Zero

Question 5

What is the expression for the electric dipole moment $$\vec{p}$$?

Accepted Answer

$$\vec{p} = q \vec{d}$$

Question 6

A disk of radius $$r = 0.10\,	ext{m} is $$placed in a uniform electric field $$E = 1.0 	imes 10^3$\,	ext{N/C} at an $$angle $$30^\circ to $$the field. What is the electric flux through the disk?

Accepted Answer

$$\Phi_E = 27\,	ext{N m}^2/	ext{C}$$

Question 7

Which equation represents Gauss’s Law?

Accepted Answer

$$\Phi_E = \oint \vec{E} \cdot d\vec{S} = \frac{Q_{	ext{enclosed}}}{\$$epsilon_0$$}$$

Question 8

If the net charge inside a closed surface is zero, what is the net electric flux through the surface?

Accepted Answer

Zero

Question 9

For a uniform electric field $$\vec{E}$$ passing through a flat surface of area $$A at an $$angle $$\phi to $$the normal, what is the electric flux?

Accepted Answer

$$\Phi_E = E A \cos \phi$$

Question 10

A closed surface (Gaussian surface) encloses charges $$+4.0\,\mu	ext{C}$$, $$+6.0\,\mu	ext{C}$$, and $$-10.0\,\mu	ext{C}. $$What is the net electric flux through the surface?

Accepted Answer

$$\Phi_E = 0$$

Question 11

Which of the following best describes the relationship between electric field lines and electric flux?

Accepted Answer

The density of electric field lines represents the magnitude of the electric field, and the electric flux is the amount of field passing through a surface.

Question 12

If the angle between the electric field $$\vec{E}$$ and the area vector $$\vec{A} is$$ $$90^\circ$$, what is the electric flux through the surface?

Accepted Answer

Zero

Question 13

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

Accepted Answer

Calculating the electric field inside a conductor

Question 14

A student claims that the electric flux through a closed surface is always positive. Is this correct?

Accepted Answer

No, the electric flux can be positive, negative, or zero depending on the net charge enclosed.

Question 15

Which equation is used to calculate the electric flux through a non-uniform electric field over a curved surface?

Accepted Answer

$$\Phi_E = \int \vec{E} \cdot d\vec{A}$$

Question 16

A dipole is aligned perpendicular to a uniform electric field. What is the magnitude of the torque acting on it?

Accepted Answer

$$	au = p E$$

Question 17

Which of the following statements about electric flux is correct?

Accepted Answer

Electric flux depends on both the magnitude of the electric field and the orientation of the surface.

Question 18

A Gaussian surface encloses a charge distribution. If the electric field is known everywhere on the surface, what can be determined using Gauss’s Law?

Accepted Answer

The net charge enclosed by the surface

Question 19

If a surface is open (not closed), which of the following statements about electric flux is true?

Accepted Answer

The electric flux through an open surface is not related to the net charge enclosed.

Electric Dipoles, Torque, and Gauss's Law: Study Notes

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