In one plane with a long straight wire through which a current I = 50 A flows, a rectangular frame is located

In one plane with a long straight wire through which a current I = 50 A flows, a rectangular frame is located so that its two large sides with a length of l = 65 cm are parallel to the wire, and the distance from the wire to the nearest of these sides is equal to its width. Determine the magnetic flux penetrating the frame.

Let’s write the formula for the solution:
Ф = B * d * S;
Let’s write down the formula for finding the magnetic induction:
B = (n0 * I) / 2 * n * x;
Let’s combine the two formulas:
d * Ф = B * (x) * d * S;
To calculate, we split S into narrow elements: d * S = l * d * x;
Let’s compose a formula for calculating the magnetic flux:
d * Ф = ((n0 * I) / 2 * n * x) * I * d * x;
Let’s integrate the expression from x = a to x = 2 * a;
Let’s find Ф:
Ф = ((n0 * I * I) / 2 * n * x) * (d * x / x) = ((n0 * I * I) / 2 * n) * I * n * x;
Let’s substitute the limits:
Ф = ((n0 * I * I) / 2 * n) * l * n * 2;
We get:
Ф = 4.5 μWb.
Answer: Ф = 4.5 μVb.