Question 1

A disk of radius $$R$$ and uniform surface charge density $$\sigma is $$shown above. What is the electric potential $$V at a $$distance $$z$$ above the center of the disk?

Accepted Answer

$$V = \frac{\sigma}{2\$$epsilon_0$$} \left( \sqrt{R^2$ + z^2$} - z \right)$$

Question 2

Which mathematical procedure is most appropriate for finding the electric potential above the center of a uniformly charged disk?

Accepted Answer

Divide the disk into infinitesimal rings and integrate their contributions using superposition.

Question 3

If the radius $$R of $$the disk is much larger than the distance $$z$$ above its center ($$R \gg z$$), what does the electric potential $$V$$ approach?

Accepted Answer

$$V \approx \frac{\sigma}{2\$$epsilon_0$$} (R)$$

Question 4

What is the direction of the electric field at a point located a distance $$z$$ above the center of a uniformly charged disk?

Accepted Answer

Perpendicular to the disk, pointing away from the disk if $$\sigma \u003e 0$$

Question 5

Given the electric potential $$V(z)$$ above the center of a disk, how do you find the electric field $$E_z at $$that point?

Accepted Answer

$$E_z = -\frac{\partial V}{\partial z}$$

Question 6

A disk of radius $$R$$ and surface charge density $$\sigma$$ produces an electric field $$E_z at a $$distance $$z$$ above its center. Which expression correctly gives $$E_z$$?

Accepted Answer

$$E_z = \frac{\sigma}{2\$$epsilon_0$$} \left( 1 - \frac{z}{\sqrt{R^2$ + z^2$}} \right)$$

Question 7

Four point charges $$Q$$ are placed at the corners of a square of side $$a. $$What is the electric potential at the center of the square?

Accepted Answer

$$V = \frac{4Q}{4\pi\$$epsilon_0$$ \sqrt{2} a}$$

Question 8

Which principle allows you to calculate the electric potential at the center of a square due to four charges at its corners?

Accepted Answer

Superposition principle

Question 9

If each charge at the corners of a square is $$Q$$, and the side length is $$a$$, what is the distance from each charge to the center?

Accepted Answer

$$\frac{a}{\sqrt{2}}$$

Question 10

A student calculates the electric field above a disk by differentiating the potential with respect to $$z. $$Which formula should they use?

Accepted Answer

$$E_z = -\frac{\partial V}{\partial z}$$

Question 11

In a real-world scenario, a medical device uses a charged disk to create an electric field for therapy. If the disk has radius $$R$$ and surface charge density $$\sigma$$, what is the field at a point $$z$$ above its center?

Accepted Answer

$$E_z = \frac{\sigma}{2\$$epsilon_0$$} \left( 1 - \frac{z}{\sqrt{R^2$ + z^2$}} \right)$$

Question 12

Which of the following is a critical step in solving for the electric potential above a disk?

Accepted Answer

Integrate over the disk using polar coordinates

Question 13

A disk of radius $$R$$ and surface charge density $$\sigma is $$used in a sensor. If the sensor measures the potential at $$z$$ above the disk, which formula should it use?

Accepted Answer

$$V = \frac{\sigma}{2\$$epsilon_0$$} \left( \sqrt{R^2$ + z^2$} - z \right)$$

Electric Potential and Field of Charged Disk & Square Charge Configuration

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