Find the magnetic field at the center of the square. |...

Name: Problem 83, Chapter 19: Physics
Uploaded: 2021-07-20T17:02:21-08:00
Duration: 8 min 23 s
Channel: Vishal Gupta
Description: Find the magnetic field at the center of the square.

Key Concepts

Superposition Principle

The superposition principle states that the net magnetic field at any point is the vector sum of the magnetic fields produced by all individual current elements. This principle is especially important when calculating fields in systems with multiple segments, as it enables the separate evaluation of contributions from each segment before summing them to obtain the total field.

Symmetry in Magnetic Field Calculations

Symmetry plays a critical role when determining the magnetic field in configurations like a square loop. Recognizing symmetrical elements in the geometry allows for significant simplifications in the calculation, as it identifies equal contributions from various segments and sometimes leads to cancellations of field components that are oriented in opposite directions.

Biot-Savart Law

The Biot-Savart Law is a fundamental principle used to compute the magnetic field produced at a point by a small segment of current. It involves an integration over the distance between the current element and the observation point, making it essential for evaluating fields generated by complex current distributions such as loops or finite wire segments.

Transcript

00:01 Hi, in the given problem, four conductors are carrying current in the same direction and they are arranged such as to pass through the corners of a square.

00:16 So first of all, we show this is square here.

00:22 Suppose the square is lying in the plane of paper, means we are showing cross -sectional view of this arrangement of four conductors.

00:32 The upper two conductors are carrying current which is coming out of the plane of paper perpendicularly and the lower two conductors are carrying current which is directed into the plane of paper perpendicularly.

00:51 Suppose these corners are named as a, b, c and d.

00:59 The side length of this square is d now the magnitude of current passing through all these four conductors the same current is passing through all of them and it is having a value of 10 .0 ampere and the side length of the square is 0 .1 meter so it's diagonal the diagonal of this square will be given as whether it is ac or it is bd that is side root 2 means d into root 2 meter means this is 0 .10 into 1 .1 1 .414 meter and it will become 0 .14 meter so in this problem as we have to find the next magnetic field at the center of this square suppose the center is represented as o so the distance of all these current carrying conductors from the center will be equal to half of the length of the diagonal means this is 0 .14 by 2 meter and it will come out to be 0 .07 meter now using right -hand thumb rule which is the rule to find the direction of magnetic field around a straight current carrying conductor.

02:40 So using right hand thumb rule, the directions of magnetic fields due to the currents passing through the conductors at.

03:33 The corners a, b, c and d are as shown in the figure...

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