Q: If the electric field $\vec{E}$ makes an angle $\theta$ with the normal to a surface of area $A$, what is the correct expression for the electric flux through the surface?

$\Phi = |\vec{E}| |A| \cos\theta$

Question 1

Which equation correctly expresses the electric field $\vec{E}$ at a distance $r$ from a point charge $q$ in vacuum?

Accepted Answer

$\vec{E} = \dfrac{q}{4\pi\epsilon_0 r^2} \hat{r}$

Question 2

A uniformly charged ring of radius $R$ has total charge $Q$. What is the direction of the electric field at a point along the axis passing through the center of the ring?

Accepted Answer

Along the axis of the ring (z-direction)

Question 3

For a uniformly charged disk of radius $R$ and surface charge density $\sigma$, what is the correct expression for the infinitesimal charge element $dq$ used in calculating the electric field along the axis?

Accepted Answer

$dq = \sigma dA = \sigma 2\pi r dr$

Question 4

Which of the following best explains why the electric field on the axis of a uniformly charged ring only has a z-component?

Accepted Answer

The ring's charge cancels the field in the radial direction due to symmetry.

Question 5

What is the electric field far from a uniformly charged ring (distance $z \gg R$) along its axis?

Accepted Answer

$\vec{E}(z) = \dfrac{Q}{4\pi\epsilon_0 z^2} \hat{z}$

Question 6

A large, flat, uniformly charged plane has surface charge density $\sigma$. What is the electric field at a distance $z$ from the plane, assuming the plane is infinite?

Accepted Answer

$E(z) = \dfrac{\sigma}{2\epsilon_0}$

Question 7

Which formula gives the electric flux $\Phi$ through a flat surface of area $A$ when the electric field $\vec{E}$ is perpendicular to the surface?

Accepted Answer

$\Phi = E \cdot A$

Question 8

If the electric field $\vec{E}$ makes an angle $	heta$ with the normal to a surface of area $A$, what is the correct expression for the electric flux through the surface?

Accepted Answer

$\Phi = |\vec{E}| |A| \cos	heta$

Question 9

A non-flat surface is exposed to a non-uniform electric field. Which integral correctly calculates the total electric flux through the surface?

Accepted Answer

$\Phi_{total} = \int \vec{E} \cdot d\vec{A}$

Question 10

What is the sign of the electric flux through a surface if the electric field points in the same direction as the surface's area vector?

Accepted Answer

Positive

Question 11

A cube is placed in a uniform electric field such that the field lines enter one face and exit the opposite face. What is the total electric flux through the cube?

Accepted Answer

Zero

Question 12

Which of the following scenarios would result in a negative electric flux through a surface?

Accepted Answer

The electric field points opposite to the area vector of the surface.

Question 13

A charged disk of radius $R$ and surface charge density $\sigma$ produces an electric field along its axis. Which expression correctly represents the infinitesimal charge element $dq$ in terms of $r$ and $dr$?

Accepted Answer

$dq = \sigma 2\pi r dr$

Question 14

For a circular ring of radius $R$ with linear charge density $\lambda$, what is the correct expression for the infinitesimal charge element $dq$?

Accepted Answer

$dq = \lambda ds$

Question 15

Which symmetry principle allows you to simplify the calculation of the electric field at the center of a ring of charge?

Accepted Answer

Equal and opposite components of the field cancel in directions perpendicular to the axis.

Question 16

A student claims that the electric flux through a surface is always positive. Which scenario disproves this claim?

Accepted Answer

When the electric field points into the surface (opposite to the area vector)

Question 17

If the electric field is not constant over a surface, how should the total electric flux be calculated?

Accepted Answer

By integrating $\vec{E} \cdot d\vec{A}$ over the surface

Question 18

A hospital uses a large, flat, charged plate to create a uniform electric field for sterilization. If the plate has surface charge density $\sigma$, what is the magnitude of the field near the plate?

Accepted Answer

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

Question 19

Which of the following is true about the electric flux through a closed surface in a uniform electric field with no enclosed charge?

Accepted Answer

The total flux is zero.

Electric Fields and Electric Flux: Concepts, Calculations, and Applications

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