Gauss Law Cylinder, Infinite Line of Charge, Electric Flux & Field, Physics Problems

TL;DR

An imaginary cylinder with specific dimensions is used to calculate the total charge enclosed and the electric flux from an infinite line of charge.

Transcript

so how can we solve this problem an imaginary cylinder with radius 0.35 meters and length 1.5 meters has an infinite line of charge with a linear charge density of 75 nano coulombs per meter what is the total charge enclosed by the gaussian cylinder so first let's draw a picture so let's say if we have an infinite long line of charge and we're goin... Read More

Key Insights

• 🈂️ The total charge enclosed by a Gaussian cylinder can be calculated by multiplying the linear charge density and the length of the charge within the cylinder.
• 👮 The electric flux through the cylinder can be calculated using Gauss's law, which relates the flux to the total charge enclosed.
• 🫥 The electric field from an infinite line of charge is perpendicular to the surface and can be calculated using the equation lambda/(2πrε₀).
• 🔌 The lateral area of the cylinder is used to calculate the electric flux, as the top and bottom circles have no electric field passing through them.

Questions & Answers

Q: How can the total charge enclosed by a Gaussian cylinder be calculated?

The total charge enclosed can be found by multiplying the linear charge density by the length of the line of charge within the cylinder.

Q: What equation is used to calculate the electric flux through the cylinder?

Gauss's law is used to calculate the electric flux, which states that the total electric flux is equal to the total charge enclosed divided by epsilon sub naught.

Q: Is the electric flux through the cylinder inward or outward?

Since the cylinder encloses a positive charge, the electric flux is outward. If the charge was negative, the flux would be inward.

Q: How can the electric field at a certain distance from the line of charge be calculated?

The formula for the electric field from an infinite line of charge is derived using Gauss's law and then used to calculate the field for a given distance.

Summary & Key Takeaways

• An imaginary cylinder with a radius of 0.35 meters and a length of 1.5 meters is considered.

• The linear charge density of the infinite line of charge is given as 75 nano coulombs per meter.

• Part A: The total charge enclosed by the Gaussian cylinder is calculated to be 1.125 x 10^-7 coulombs.