Gauss's Law Problems - Conducting Sphere, Spherical Conductor, Electric Flux & Field, Physics

TL;DR

A detailed explanation of how to calculate the total charge on a sphere and the electric field at different distances from the center.

Transcript

a spherical conductor with radius 40 centimeters has a surface charge density of 20 micro coulombs per square meter what is the total charge on the sphere so first let's draw a picture so let's say this is the sphere and surrounding the sphere is a gaussian surface now all of the positive charge will lie on the surface of the sphere and the sphere ... Read More

Key Insights

• 🈂️ Surface charge density is the ratio between the total charge on a sphere and the surface area.
• 👮 Gauss's law relates the electric flux and the total charge enclosed by a Gaussian surface.
• 🦔 The electric field at the edge of a Gaussian surface can be calculated using the surface charge density and the radii of the spherical conductor and Gaussian surface.
• 🏑 The equation for the electric field of a point charge, k*q/r^2, can be used to calculate the electric field of a spherical conductor outside the conductor.
• 🏑 Inside a spherical conductor, the electric field is zero.
• 🏑 The electric field at a distance from the center of a spherical conductor can be calculated using Gauss's law or the equation for the electric field of a point charge.
• 🈂️ The total charge on a sphere is not dependent on its radius.

Questions & Answers

Q: How can the total charge on a spherical conductor be calculated?

The total charge can be calculated by multiplying the surface charge density by the surface area of the sphere.

Q: What is Gauss's law used for?

Gauss's law is used to calculate the electric flux passing through a Gaussian surface, which is equal to the total charge enclosed divided by the electric constant.

Q: Is the total charge on a sphere dependent on its radius?

No, the total charge on a sphere is independent of its radius. It is determined solely by the surface charge density.

Q: What happens to the electric field inside a spherical conductor?

The electric field inside a spherical conductor is zero, as there is no enclosed charge inside the conductor. The electric field only exists outside the conductor.

Summary & Key Takeaways

• A spherical conductor with a radius of 40 centimeters has a surface charge density of 20 microcoulombs per square meter.

• The total charge on the sphere can be calculated using the surface charge density and the surface area of the sphere.

• The electric field at a distance of 1.5 meters from the center of the sphere can be calculated using Gauss's law and the equation for the electric field of a point charge.