Find the magnitude of the magnetic flux through the floor of...

Find the magnitude of the magnetic flux through the floor of a house that measures $22 \mathrm{~m}$ by $18 \mathrm{~m}$. Assume that the Earth's magnetic field at the location of the house has a north-pointing horizontal component of $2.6 \times 10^{-5} \mathrm{~T}$ and a downward vertical component of $4.2 \times 10^{-5} \mathrm{~T}$.

Key Concepts

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given area. It is defined as the surface integral of the magnetic field over an area, and it quantifies the number of magnetic field lines penetrating that area. The concept is widely used in electromagnetism, especially in Faraday's law of electromagnetic induction.

Area Vector

An area vector is a vector quantity assigned to a surface, with its magnitude equal to the area of the surface and its direction perpendicular to the surface. In problems involving magnetic flux, the area vector is used to determine how much of the magnetic field passes through the surface by taking the dot product with the field vector.

Dot Product in Magnetic Flux Calculation

The computation of magnetic flux involves taking the dot product between the magnetic field vector and the area vector of the surface. This operation effectively projects the magnetic field onto the direction normal to the surface, capturing the component of the field that contributes to the flux. The dot product is central to determining how the orientation of the field relative to the surface affects the flux.

Decomposition of the Magnetic Field

In many applications, the magnetic field is not aligned with the surface of interest, so it is often necessary to decompose it into components. By breaking the field into perpendicular and parallel parts, one can isolate the component that is relevant for calculating the flux through a given surface. This decomposition is essential in accurately applying the concept of magnetic flux in various scenarios.

Transcript

00:02 Kid, we're told to find the magnitude of the magnetic field.

00:06 Or did my very flocks trudy's floor here, given by these dimensions 18 meters between two meters on we we are zoomed at the it's my grand nephew at this location has a result our complaint off 2.8 times 10 to the negative five case lands and find school downward component 4.2 time state in a negative five this'll ass on.

00:40 Um, we know the normal to this floor here.

00:45 No matter is just gonna be a narrow pointing.

00:47 They were from that.

00:49 Sophie's proper medical answered our sophie's on dde.

00:54 The magnetic flux is equal to the magnetic field times.

01:00 Yeah, course signed the angle between the flocks.

01:06 Of course.

01:06 I'm the angle between the field under normal to sophie's.

01:15 So, um, this horizontal component that an angle 90 degrees to this normal and so cost 90 equals zero.

01:30 So it means is my, uh, this magnetic field there isn't i'll come over to my nephew doesn't create any magnetic flux jury component of the mind.

01:42 Many feel that creating magnetic flux is this component off the feud device cow down with pointing.

01:51 Um component that is in the same direction asked to normal.

01:57 So cause of 00 because the angle between them zero course of zero is one.

02:04 So the net magnetic flux she's gonna be zero due to these areas and talk open and close...

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