Find the magnetic field at point P, the midpoint of the top side of the square.

Name: Problem 84, Chapter 19: Physics
Uploaded: 2021-07-20T17:03:16-08:00
Duration: 9 min 57 s
Channel: Vishal Gupta
Description: Find the magnetic field at point P, the midpoint of the top side of the square.

Find the magnetic field at point P, the midpoint of the top...

Key Concepts

Symmetry in Magnetic Field Calculations

Using symmetry in magnetic field problems helps to simplify the calculations by identifying components of the field that cancel out or combine uniformly. In problems involving simple geometric shapes like squares or circles, symmetry arguments can reduce the complexity of the integrals, making it easier to compute the net field at specific points.

Principle of Superposition

The principle of superposition states that the total magnetic field created by multiple current segments is the vector sum of the magnetic fields produced by each segment individually. This is particularly useful in complex geometries, such as current loops or square configurations, where symmetry and multiple contributions can simplify the analysis.

Magnetic Field from Finite Current Elements

This concept involves applying the Biot-Savart Law to calculate the magnetic field produced by segments of a finite length. Since the magnetic field produced by a finite wire differs from that of an infinite wire, integration over the length of the conductor is necessary. The resulting expressions take into account the geometry of the current path relative to the observation point.

Biot-Savart Law

The Biot-Savart Law is a fundamental principle used to calculate the magnetic field produced by a small segment of a current-carrying conductor. It expresses the infinitesimal contribution of a current element to the magnetic field at a point in space. This law is important for determining the field from non-uniform or finite current distributions and involves integrating over the current path.

Transcript

00:01 Hi, in the given problem, similar to the previous problem, problem number 83, here, we are also considering the given setter and the cross -sectional view of the given setter, and that is in the form of a square and the four current carrying conductors are at the corners of this square.

00:26 The upper two conductors are carrying current which is coming out of the plane of paper, and the lower two conductors are carrying current which is getting into the plane of paper.

00:36 Here these corners are named as a, b, c and d.

00:42 The side length of this square is d.

00:45 Here the value of this d is 0 .1, 0 meter and current passing through each of the conductor is 10 .0 amper.

00:57 Here in this problem the observation point is p, which is at the midpoint of the upper most side.

01:07 Now, if you look for the various magnetic fields here, using right -hand thumb rule, the directions of various magnetic fields.

01:43 Due to the conductors, current carrying conductors kept at the four corners of the square, the four magnetic fields are as shown in the figure.

01:59 So, if we draw these magnetic fields, first of all, magnetic field due to the conductor at a, that is going up in the plane of paper.

02:13 And the magnetic field due to the conductor at b, that will be going down in the plane of paper.

02:22 So here this is b, a, and here this is b, b.

02:27 B.

02:29 Now as the distance because this is the midpoint so this distance are is same from both of these current carrying conductors and current is also same so the magnetic field b a will be equal in magnitude to that b b and direction is opposite so they cancel each other as we have to find net magnetic field at point p so here this magnetic field these two magnetic fields cancel each other now the other two conductors first of all if we look at the conductor put at this point d the magnetic field due to the conductor here we have named this point as c and here here we have named this point as d so, now the magnetic field due to this c, that is perpendicular to the line joining of this conductor 2 .p.

03:48 And the direction of magnetic field will be perpendicular to this.

03:52 Here this is b c...

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