Suppose you have a magnetic field $\vec{B} = 0.6 \text{ mT } \hat{x}$. Three identical square loops with side lengths $L = 0.5 \text{ m}$ are situated as shown below. The perspective shows a side view of the square loops, so they appear very thin even though they are squares when viewed face on.

Square Loops in the B-field

• The orientations of the square loops are as indicated above. They can be described by their angles with respect to the magnetic field. $\theta_1 = 0$, $\theta_2 = 90^\text{o}$, $\theta_3 = 42^\text{o}$.
• The magnetic field is $\vec{B} = 0.6 \text{ mT } \hat{x}$.
• The length of a square's side is $L = 0.5 \text{ m}$.

• The magnetic flux through each loop.

• The loops have flat faces.
• The magnetic field does not change with time, and is uniform in space.

• We represent magnetic flux through an area as

$$\Phi_B = \int \vec{B} \bullet \text{d}\vec{A}$$

• We represent the situation with the given representation in the example statement above. Below, we also show a side and front view of the first loop for clarity.

First Loop

Since the magnetic field has a uniform direction, and the area of the loop is