Two similar coils of radius R and number of turns N are lying concentrically with their planes at right angles to each other.The currents flowing in them are I and √3I respectively.The resultant magnetic induction at the center will be?

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Two similar coils of radius R and number of turns N are lying concentrically with their planes at right angles to each other.The currents flowing in them are I and √3I respectively.The resultant magnetic induction at the center will be?

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Two similar coils of radius R and number of turns N are lying concentr...

Problem Statement

Two concentric coils of radius R and number of turns N are lying with their planes at right angles to each other. The currents flowing in them are I and √3I respectively. Find the resultant magnetic induction at the center.

Solution

To find the resultant magnetic induction at the center, we will use the formula for the magnetic field produced by a current-carrying coil:

B = μ₀NI/2R

where B is the magnetic field, μ₀ is the permeability of free space, N is the number of turns, I is the current, and R is the radius of the coil.

Magnetic Field of the First Coil

The magnetic field produced by the first coil can be found using the formula:

B₁ = μ₀NI/2R

Substituting the given values, we get:

B₁ = μ₀NI/2R = (4π × 10⁻⁷ T m/A)(N)(I)/(2R)

B₁ = 2π × 10⁻⁷ N I/R

Magnetic Field of the Second Coil

The magnetic field produced by the second coil can be found using the same formula:

B₂ = μ₀N(√3I)/2R

Substituting the given values, we get:

B₂ = μ₀N(√3I)/2R = (4π × 10⁻⁷ T m/A)(N)(√3I)/(2R)

B₂ = √3π × 10⁻⁷ N I/R

Resultant Magnetic Field

Since the two coils are at right angles to each other, the magnetic field vectors produced by them will be perpendicular to each other. Therefore, we can use the Pythagorean theorem to find the magnitude of the resultant magnetic field:

B = √(B₁² + B₂²)

Substituting the values of B₁ and B₂, we get:

B = √[(2π × 10⁻⁷ N I/R)² + (√3π × 10⁻⁷ N I/R)²]

B = √(4π²/3) × 10⁻¹⁴ N I/R

B = (2/√3)π × 10⁻⁷ N I/R

Final Answer

Therefore, the resultant magnetic induction at the center is (2/√3)π × 10⁻⁷ N I/R.

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Two similar coils of radius R and number of turns N are lying concentrically with their planes at right angles to each other.The currents flowing in them are I and √3I respectively.The resultant magnetic induction at the center will be? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Two similar coils of radius R and number of turns N are lying concentrically with their planes at right angles to each other.The currents flowing in them are I and √3I respectively.The resultant magnetic induction at the center will be? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two similar coils of radius R and number of turns N are lying concentrically with their planes at right angles to each other.The currents flowing in them are I and √3I respectively.The resultant magnetic induction at the center will be?.

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