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

  • Parallel to the x-axis
  • In the direction of the current element
  • Perpendicular to the x-axis
  • Perpendicular to the plane formed by dl⃗ and r⃗ (correct)

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

  • They are in mutually opposite directions (correct)
  • They add up constructively
  • They are parallel to the x-axis
  • They are perpendicular to the x-axis

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

  • Inversely proportional (correct)
  • Directly proportional
  • No relationship
  • Exponentially proportional

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

    <p>dB cos  components are parallel to x-axis</p> Signup and view all the answers

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

    <p>$dB = \mu_0 \frac{I dy}{2\pi r}$</p> Signup and view all the answers

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

    <p>Along the z-axis</p> Signup and view all the answers

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

    <p>$B = \frac{\mu_0 I}{2\pi} ln(1+\theta)$</p> Signup and view all the answers

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

    <p>$r = y tan \theta$</p> Signup and view all the answers

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

    <p>B⃗ = ∇⃗ × A⃗</p> Signup and view all the answers

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

    <p>B⃗ = μπ ⃗× ∫</p> Signup and view all the answers

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

    <p>μπ ∫ ⃗</p> Signup and view all the answers

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

    <p>Because it doesn't vary like electric potential V</p> Signup and view all the answers

    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.

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