# 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?

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

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?

$r = y tan \theta$

B⃗ = ∇⃗ × A⃗

B⃗ = μπ ⃗× ∫

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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