Magnetic Energy and Cylinder Volume

The video tutorial explains how to calculate the energy stored in an inductor and a magnetic field. It begins with an example of a 15-amp current flowing through a 200 millihenry inductor, calculating the energy stored as 22.5 joules. The tutorial then derives the formula for magnetic energy density in a 4.5 tesla magnetic field, resulting in 8.057 x 10^6 joules per cubic meter. Finally, it calculates the energy stored in a magnetic field confined within a cylinder, using the derived energy density and the cylinder's volume.

What is the formula for calculating the energy stored in an inductor?

• 0.5 * I^2 / L

• L * I^2

• L^2 * I

• 0.5 * L * I^2

If an inductor has an inductance of 200 millihenries and a current of 15 amps, what is the energy stored in it?

• 45 joules

• 15 joules

• 30 joules

• 22.5 joules

What is the formula for magnetic energy density in a magnetic field?

• B / (2 * mu_0)

• B^2 / (2 * mu_0)

• B^2 * mu_0 / 2

• 2 * B^2 * mu_0

For a magnetic field of 4.5 tesla, what is the calculated magnetic energy density?

• 4.5 x 10^6 J/m^3

• 2.5 x 10^6 J/m^3

• 10 x 10^6 J/m^3

• 8.057 x 10^6 J/m^3

What is the unit of magnetic energy density?

• Joules per cubic meter

• Joules per square meter

• Joules per meter

• Joules per liter

What is the value of mu_0 used in the calculations?

• 4 pi x 10^-6

• 2 pi x 10^-7

• 4 pi x 10^-7

• 2 pi x 10^-6

What is the formula for the potential energy stored in a magnetic field in terms of energy density and volume?

• Energy density - Volume

• Energy density * Volume

• Energy density + Volume

• Volume / Energy density

How do you calculate the volume of a cylinder?

• 2 * pi * r * height

• pi * r^2 * height

• pi * r^2 / height

• pi * r * height

If a cylinder has a radius of 0.2 meters and a height of 1.5 meters, what is its volume?

• 0.094 m^3

• 0.282 m^3

• 0.376 m^3

• 0.188 m^3

What is the total potential energy stored in a cylinder with a magnetic field of 4.5 tesla, radius of 0.2 meters, and height of 1.5 meters?

• 2.5 x 10^6 joules

• 1.5 x 10^6 joules

• 2.0 x 10^6 joules

• 1.0 x 10^6 joules