Magnetic Flux passing through loop

[uzair_ha91]

Homework Statement

The magnetic field in a certain region is given by B=<40i-18k>T. How
much flux passes through a 5cm^2 area loop in this region if the loop
lies flat in the xy plane?

Homework Equations

Flux=B.A

The Attempt at a Solution

I got the answer (90 * 10^-4) in negative, and its in positive in the textbook at the back...
How can flux be negative and why can we drop the negative sign?

 

[Gib Z]

The amount of flux can be thought of as always a positive quantity, whilst the sign of the value dictates direction based on a previously decided convention. For example, if we define Up to be the positive direction, and we have 5 Wbs of flux downwards, we can express that as -5 Wbs. The sign tells you the direction the flux acts in, the sign tells you the direction.

 

[tomcue]

I understand your confusion about the negative sign in the flux calculation. The negative sign in this case indicates the direction of the flux, not its magnitude. Flux is a vector quantity, meaning it has both magnitude and direction. In this case, the negative sign indicates that the flux is directed downwards, perpendicular to the xy plane.

To understand why we can drop the negative sign, we need to look at the definition of flux. Flux is defined as the amount of a vector field passing through a given surface. In this case, the surface is a 5cm^2 area loop lying flat in the xy plane. The direction of the flux is determined by the direction of the magnetic field, which is given as B=<40i-18k>T. The negative sign in the magnetic field vector indicates that the magnetic field is directed downwards.

Now, when we calculate the flux using the formula Flux=B.A, we get a negative value because the area vector A is directed upwards, opposite to the direction of the magnetic field. However, since we are only interested in the magnitude of the flux, we can drop the negative sign and simply take the absolute value of the calculated flux. This gives us a positive value, which is the magnitude of the flux passing through the loop.

In conclusion, the negative sign in the flux calculation is simply indicating the direction of the flux, and we can drop it when we are only interested in the magnitude of the flux. I hope this clears up any confusion and helps you understand the concept of flux passing through a loop in a magnetic field.