A infinite wire carrying a current 5A is bent at right angle find the magnetic Induction at a point on the perpendicular to the wire through its point of bending at a distance 35 cm from the corner

Hmmmm. Wondering what exactly is perpendicular at the corner?

To find the magnetic induction (magnetic field) at a point on the perpendicular to the wire through its point of bending, we can use the Biot-Savart Law. The law states that the magnetic field created by a small segment of a current-carrying wire is directly proportional to the magnitude of the current, the length of the wire segment, and the sine of the angle between the wire segment and the line connecting the point to the wire.

In this case, since the wire is infinite, we can consider a small segment of the wire. Let's call the segment "dl". From the given information, we know that the current through the wire is 5A.

Now, let's consider the small segment of the wire that is closest to the point where we want to find the magnetic induction. The length of this segment (dl) will be infinitesimally small, but we will still consider it for calculations.

To find the magnetic induction at the point, we need to integrate the contributions from all the infinitesimally small segments of the wire along the path perpendicular to the wire through the point of bending.

To express this mathematically, we can say that the magnetic induction (dB) at the point is given by the integral of the Biot-Savart Law over the entire length of the wire:

dB = (μ₀/4π) * (I * dl * sinθ) / r²

Where:
- dB is the magnetic induction at the point,
- μ₀ is the permeability of free space (a constant with a value of 4π x 10⁻⁷ Tm/A),
- I is the current (5A in this case),
- dl is the length of the wire segment,
- θ is the angle between the wire segment and the line connecting the point to the wire,
- r is the distance between the small wire segment and the point.

To solve this problem, we need to find the contribution of each infinitesimally small segment of the wire and integrate it over the entire length of the wire. However, since the wire is infinite, we can simplify the problem by realizing that the contributions from the segments on one side of the bend will cancel out the contribution of the segments on the other side of the bend, leaving only the segment closest to the point. Thus, we can consider only the segment closest to the point and ignore the other segments.

Now, let's calculate the magnetic induction using the given information.

Given:
Current, I = 5A
Distance from the corner, r = 35cm = 0.35m

Since we are considering the segment closest to the point, the angle θ will be 90 degrees (right angle).

Substituting the given values into the Biot-Savart Law equation:

dB = (μ₀/4π) * (I * dl * sinθ) / r²
= (4π x 10⁻⁷ Tm/A) * (5A) * dl / (0.35m)²

Since we are considering an infinitesimally small segment, dl does not contribute to the overall calculation. Therefore, we can ignore it for the final result:

dB = (4π x 10⁻⁷ Tm/A) * (5A) / (0.35m)²

Evaluating this expression will give us the magnetic induction at the point on the perpendicular line through the wire's point of bending at a distance of 35cm from the corner.