Two similar coils are kept mutually perpendicular such that...

Two similar coils are kept mutually perpendicular such that their centers co-inside. At the centre, find the ratio of the mag. field due to one coil and the resultant magnetic field by both coils, if the same current is flown.
(a) $1: \sqrt{2}$
(b) $1: 2$
(c) $2: 1$
(d) $\sqrt{3}: 1$

Key Concepts

Magnetic Field of a Circular Loop

This concept deals with the magnetic field produced at the center of a circular current-carrying coil. It is derived using the Biot-Savart law and involves the physical parameters of the coil like its radius and the magnitude of the current. The field at the center is directed perpendicular to the plane of the loop, and its magnitude can be written in terms of fundamental constants and the current, making it a fundamental concept in electromagnetism.

Superposition Principle

In electromagnetism, the superposition principle states that the net field caused by multiple sources is the vector sum of the fields produced by each source individually. This principle is essential in calculating the resultant magnetic field when there are two or more current distributions, even when these distributions are oriented in different directions.

Vector Addition in Perpendicular Directions

When two magnetic fields are produced by coils that are oriented perpendicularly, their individual fields at a common point can be added using vector addition rules, typically resulting in the use of the Pythagorean theorem. This is important for determining the magnitude of the resultant field, as fields that are orthogonal combine to produce a resultant whose magnitude is the square root of the sum of the squares of the individual field magnitudes.

Transcript

Please give Ace some feedback