Electric Field Due to a Charged Disk, Infinite Sheet of Charge, Parallel Plates - Physics Problems

TL;DR

This video explains how to calculate the electric field due to a charged disk and shows how the formula can be applied to an infinite sheet of charge and parallel plates.

Transcript

in this video we're going to focus on calculating the electric field due to a charged disk we're going to derive the formula and from that formula we're going to come up with a formula to calculate the electric field of an infinite sheet of charge and also the electric field between two parallel plates of that contain a sheet of charge an infinite ... Read More

Key Insights

• 👈 The electric field of a small segment of charge on a disk can be calculated using the equation k times dq divided by l^2, where l is the distance from the segment to the point of interest.
• 💽 The electric field of an infinite sheet of charge can be obtained from the formula for a disk by taking the limit as the radius of the disk approaches infinity.
• 🈶 The electric field between two infinite sheets of charge is zero outside the sheets and equal to the charge per unit area divided by the permittivity of free space inside the sheets.
• 🏑 The net electric field in the y direction at a point above or below a charged disk is zero due to the cancellation of the y-components of the electric fields created by the charges on the disk.

Questions & Answers

Q: How is the electric field of a point charge related to the electric field of the small segment of charge on the disk?

The electric field of a point charge is given by Coulomb's law, while the electric field of a small segment of charge on the disk is calculated using the equation k times dq divided by l^2, where dq is the charge of the segment and l is the distance from the segment to the point of interest.

Q: Why is the net electric field in the y direction zero at point P?

The electric fields created by the charges on the top and bottom of the disk have equal magnitudes but opposite directions in the y-axis. As a result, the y-components cancel out, resulting in a net electric field of zero in the y direction at point P.

Q: How does the formula for the electric field of a disk relate to the formula for an infinite sheet of charge?

As the radius of the disk approaches infinity, the term involving X divided by the square root of X^2 + r^2 becomes negligible since X is insignificant compared to infinitely large r. Thus, the formula for the electric field of an infinite sheet of charge is derived from the formula for the electric field of a disk by taking this limit.

Q: What is the electric field between two infinite sheets of charge?

The electric field between two infinite sheets of charge is zero outside the sheets. Inside the sheets, the electric field is equal to the charge per unit area divided by the permittivity of free space.

Summary & Key Takeaways

• The video starts by deriving the formula to calculate the electric field due to a charged disk, considering the distance between the center and a point outside the disk.

• The formula for the electric field of an infinite sheet of charge is obtained by taking the limit as the radius of the disk approaches infinity.

• The video also explains that the electric field between two parallel plates with charge sheets is zero outside the plates and equal to the charge per unit area divided by the permittivity of free space between the plates.