Derivation of Magnetic Field of a Straight Wire using Biot-Savart Law

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12 Questions

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?

Perpendicular to the plane formed by dl⃗ and r⃗

Why do the components dB sin  nullify each other when calculating the magnetic field at point P?

They are in mutually opposite directions

How does the magnetic field vary with the distance from the wire according to Eqn.(5)?

Inversely proportional

Why do only dB cos  components add to each other when calculating the total magnetic field at point P?

dB cos  components are parallel to x-axis

What is the formula for the magnetic field at point P due to a small current element along a straight wire?

$dB = \mu_0 \frac{I dy}{2\pi r}$

In which direction is the magnetic field at point P if it is located at a perpendicular distance y from the straight wire?

Along the z-axis

What is the total magnetic field at point P due to the straight wire obtained by integrating?

$B = \frac{\mu_0 I}{2\pi} ln(1+\theta)$

How does the distance r from the origin change with respect to the angle θ in the context of calculating the magnetic field?

$r = y tan \theta$

In the context of the text, how can the magnetic field B⃗ be related to the Magnetic Vector Potential A⃗?

B⃗ = ∇⃗ × A⃗

What is the magnetic field due to a current carrying long straight wire as described in the text?

B⃗ = μπ ⃗× ∫

Based on the information provided, what is known as the vector potential A⃗?

μπ ∫ ⃗

Why is A⃗ known as Vector Potential as mentioned in the text?

Because it doesn't vary like electric potential V

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.

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