A circular loop (radius of 20 cm ) is in a uniform magnetic field of 0.15 T. What angle(s) bet

step 1 have a circular loop of radius r equals to 20 cm that is 0 .20 meter in a uniform magnetic field

A circular loop (radius of 20 cm ) is in a uniform magnetic...

A circular loop (radius of $20 \mathrm{~cm}$ ) is in a uniform magnetic field of $0.15 \mathrm{~T}$. What angle(s) between the normal to the plane of the loop and the field would result in a flux with a magnitude of $1.4 \times 10^{-2} \mathrm{~T} \cdot \mathrm{m}^{2} ?$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetism, taking into account the strength and the extent of a magnetic field. It is defined as the dot product of the magnetic field vector and the area vector of a surface, highlighting how much of the magnetic field passes through that surface.

Area of a Circular Loop

The area of a circular loop is calculated using the geometric formula A = ?r², where r is the radius of the circle. This area is crucial in determining the magnetic flux through the loop, as it directly influences how much of the magnetic field interacts with the loop.

Angular Dependence of Magnetic Flux

The magnetic flux through a loop is dependent on the angle between the magnetic field and the normal vector to the plane of the loop, expressed as ? = BA cos(?). This relationship shows that the flux decreases as the angle increases, since the cosine function reduces the effective component of the magnetic field passing through the loop.

Inverse Trigonometric Functions

Inverse trigonometric functions, such as the inverse cosine (arccos), are used to determine the angle when the value of the cosine of that angle is known. In the context of magnetic flux, this is used to solve for the angle between the magnetic field and the loop's normal when the flux is specified.

Transcript

Please give Ace some feedback