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Questions and Answers
What is the direction of the magnetic field dB⃗ at point P due to a current element I dl⃗ at the top of the ring?
What is the direction of the magnetic field dB⃗ at point P due to a current element I dl⃗ at the top of the ring?
Why do the components dB sin nullify each other when calculating the magnetic field at point P?
Why do the components dB sin nullify each other when calculating the magnetic field at point P?
How does the magnetic field vary with the distance from the wire according to Eqn.(5)?
How does the magnetic field vary with the distance from the wire according to Eqn.(5)?
Why do only dB cos components add to each other when calculating the total magnetic field at point P?
Why do only dB cos components add to each other when calculating the total magnetic field at point P?
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What is the formula for the magnetic field at point P due to a small current element along a straight wire?
What is the formula for the magnetic field at point P due to a small current element along a straight wire?
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In which direction is the magnetic field at point P if it is located at a perpendicular distance y from the straight wire?
In which direction is the magnetic field at point P if it is located at a perpendicular distance y from the straight wire?
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What is the total magnetic field at point P due to the straight wire obtained by integrating?
What is the total magnetic field at point P due to the straight wire obtained by integrating?
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How does the distance r from the origin change with respect to the angle θ in the context of calculating the magnetic field?
How does the distance r from the origin change with respect to the angle θ in the context of calculating the magnetic field?
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In the context of the text, how can the magnetic field B⃗ be related to the Magnetic Vector Potential A⃗?
In the context of the text, how can the magnetic field B⃗ be related to the Magnetic Vector Potential A⃗?
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What is the magnetic field due to a current carrying long straight wire as described in the text?
What is the magnetic field due to a current carrying long straight wire as described in the text?
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Based on the information provided, what is known as the vector potential A⃗?
Based on the information provided, what is known as the vector potential A⃗?
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Why is A⃗ known as Vector Potential as mentioned in the text?
Why is A⃗ known as Vector Potential as mentioned in the text?
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Study Notes
Magnetic Field and Vector Potential
- The direction of the magnetic field dB⃗ at point P due to a current element I dl⃗ at the top of the ring is determined by the right-hand rule.
- The components dB sin nullify each other when calculating the magnetic field at point P because they are perpendicular to each other and cancel out.
- The magnetic field varies inversely with the square of the distance from the wire, according to Eqn.(5), i.e., B ∝ 1/r^2.
- Only dB cos components add to each other when calculating the total magnetic field at point P because they are parallel to each other and combine to form the total field.
- The formula for the magnetic field at point P due to a small current element along a straight wire is dB = (μ₀I dl sin φ) / (4πr^2).
- The magnetic field at point P, located at a perpendicular distance y from the straight wire, is directed perpendicular to the plane containing the wire and point P.
- The total magnetic field at point P due to the straight wire is obtained by integrating the contributions from all current elements along the wire.
- The distance r from the origin changes with respect to the angle θ as r = y / sin θ, where y is the perpendicular distance from the wire to point P.
- The magnetic field B⃗ can be related to the Magnetic Vector Potential A⃗ through the equation B⃗ = ∇ × A⃗.
- The magnetic field due to a current-carrying long straight wire is described by the Biot-Savart law.
- The vector potential A⃗ is a vector field that generates the magnetic field through the curl operation.
- A⃗ is known as the Vector Potential because it has the potential to generate the magnetic field.
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Description
This quiz involves deriving the formula for the magnetic field generated by a straight wire carrying current using the Biot-Savart law. It covers the steps to calculate the magnetic field at a specific point located at a perpendicular distance from the wire.
