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Two identical coils carrying equal current have a common centre, and their planes are at right angles to each other. Find the ratio of the magnitude of the resultant magnetic field at centre and the field due to one coil alone
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Two identical coils carrying equal current have a common centre, and t...
Solution:
Given:
Two identical coils carrying equal current have a common centre, and their planes are at right angles to each other.
To find:
The ratio of the magnitude of the resultant magnetic field at centre and the field due to one coil alone.
Explanation:
When two identical coils carrying equal current have a common centre, and their planes are at right angles to each other, the magnetic field at the centre of the coils can be found as follows:
1. Magnetic field due to one coil:
The magnetic field at the centre of one coil can be found using the formula:
B = (μ₀/4π) × (2I/R)
Where,
B = Magnetic field at the centre of the coil
μ₀ = Permeability of free space = 4π × 10⁻⁷ T m/A
I = Current flowing through the coil
R = Radius of the coil
2. Magnetic field due to one coil:
The magnetic field at the centre of the two coils can be found using the formula:
B' = (μ₀/4π) × (4I/R)
Where,
B' = Magnetic field at the centre of the two coils
μ₀ = Permeability of free space = 4π × 10⁻⁷ T m/A
I = Current flowing through each coil
R = Radius of each coil
3. Resultant magnetic field:
The resultant magnetic field at the centre of the two coils can be found using the Pythagorean theorem:
B_res = √(B² + B'²)
4. Ratio of the magnitude of the resultant magnetic field and the field due to one coil alone:
The ratio of the magnitude of the resultant magnetic field at centre and the field due to one coil alone can be found using the formula:
Ratio = B_res / B
Answer:
The ratio of the magnitude of the resultant magnetic field at centre and the field due to one coil alone is √2 : 1.
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Two identical coils carrying equal current have a common centre, and their planes are at right angles to each other. Find the ratio of the magnitude of the resultant magnetic field at centre and the field due to one coil alone
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Two identical coils carrying equal current have a common centre, and their planes are at right angles to each other. Find the ratio of the magnitude of the resultant magnetic field at centre and the field due to one coil alone 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 identical coils carrying equal current have a common centre, and their planes are at right angles to each other. Find the ratio of the magnitude of the resultant magnetic field at centre and the field due to one coil alone covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical coils carrying equal current have a common centre, and their planes are at right angles to each other. Find the ratio of the magnitude of the resultant magnetic field at centre and the field due to one coil alone.
Two identical coils carrying equal current have a common centre, and their planes are at right angles to each other. Find the ratio of the magnitude of the resultant magnetic field at centre and the field due to one coil alone 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 identical coils carrying equal current have a common centre, and their planes are at right angles to each other. Find the ratio of the magnitude of the resultant magnetic field at centre and the field due to one coil alone covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical coils carrying equal current have a common centre, and their planes are at right angles to each other. Find the ratio of the magnitude of the resultant magnetic field at centre and the field due to one coil alone.
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