An element, d l=d x î (where d x=1 cm ) is placed at the origin and carries a large current i=1

step 1 Hello students in this question we have an element having dx equals to one centimeter in the I c

An element, d l=d x î (where d x=1 cm ) is placed at the...

An element, $d l=d x$ \hat{ i } (where $d x=1 \mathrm{~cm}$ ) is placed at the origin and carries a large current $i=10 \mathrm{~A}$. What is the magnetic field on the $y$-axis at a distance of $0.5 \mathrm{~m} ?$ (a) $2 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$ (b) $4 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$ (c) $-2 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$ (d) $-4 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$

An element, $d l=d x$ \hat{ i } (where $d x=1 \mathrm{~cm}$ ) is placed at the origin and carries a large current $i=10 \mathrm{~A}$. What is the magnetic field on the $y$-axis at a distance of $0.5 \mathrm{~m} ?$
(a) $2 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$
(b) $4 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$
(c) $-2 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$
(d) $-4 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}$

Key Concepts

Right-Hand Rule

The right-hand rule is a visual mnemonic used to determine the direction of the magnetic field generated by a current element. By pointing the thumb in the direction of the current and curling the fingers toward the observation point, the direction of the resulting magnetic field is indicated by the direction of the extended fingers.

Biot-Savart Law

This law provides the fundamental relationship to calculate the magnetic field produced by a small current element. It states that the differential magnetic field is proportional to the current, the differential length element, and the sine of the angle between the current element and the position vector, and inversely proportional to the square of the distance between the element and the observation point.

Current Element

A current element is an infinitesimally short segment of a current-carrying conductor. It is used in calculations involving the Biot-Savart Law to determine the magnetic field contribution from small parts of a conductor, which may then be integrated to find the field from a continuous current distribution.

Vector Cross Product

The vector cross product is crucial in the Biot-Savart Law because it accounts for the direction of the magnetic field. It produces a vector perpendicular to the plane formed by the current element and the position vector, and its magnitude is proportional to the sine of the angle between these two vectors.

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