An element d ℓ^-=dx ↑(where dx=1 cm ) is placed at the origin and carries a large current I=10

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^-=dx ↑(where dx=1 cm ) is placed at the...

An element $\mathrm{d} \ell^{-}=\mathrm{dx} \uparrow$ (where $\mathrm{dx}=1 \mathrm{~cm}$ ) is placed at the origin and carries a large current $\mathrm{I}=10 \mathrm{Amp}$. What is the mag. field on the Y-axis at a distance of $0.5$ meter ? (a) $2 \times 10^{-8} \mathrm{k} \wedge \mathrm{T}$ (b) $4 \times 10^{8} \mathrm{k} \wedge \mathrm{T}$ (c) $-2 \times 10^{-8} \mathrm{k} \wedge \mathrm{T}$ (d) $-4 \times 10^{-8} \mathrm{k} \wedge \mathrm{T}$

An element $\mathrm{d} \ell^{-}=\mathrm{dx} \uparrow$ (where $\mathrm{dx}=1 \mathrm{~cm}$ ) is placed at the origin and carries a large current $\mathrm{I}=10 \mathrm{Amp}$. What is the mag. field on the Y-axis at a distance of $0.5$ meter ?
(a) $2 \times 10^{-8} \mathrm{k} \wedge \mathrm{T}$
(b) $4 \times 10^{8} \mathrm{k} \wedge \mathrm{T}$
(c) $-2 \times 10^{-8} \mathrm{k} \wedge \mathrm{T}$
(d) $-4 \times 10^{-8} \mathrm{k} \wedge \mathrm{T}$

Key Concepts

Biot-Savart Law

The Biot-Savart Law provides the fundamental relation to calculate the magnetic field produced by a small segment of current. It expresses the magnetic field contribution as proportional to the current element and involves a cross product between the current element and the unit vector pointing from the element to the field point, divided by the square of the distance between them.

Magnetic Field Due to a Current Element

In magnetostatics, the magnetic field at a point in space is determined by summing (or integrating) the contributions from all infinitesimal current elements. Each element’s contribution depends not only on its magnitude and distance from the point but also on the angle between the current direction and the line connecting the element to the point.

Vector Cross Product in Electromagnetism

The vector cross product is crucial in determining the direction of the magnetic field generated by a current element. It combines the direction of the current with the position vector from the current to the field point, thereby ensuring that the resulting magnetic field is perpendicular to both, as dictated by the right-hand rule.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field resulting from a current element. By aligning the fingers of the right hand with the current and curling them toward the field point, the thumb points in the direction of the magnetic field, ensuring accurate sign and direction in the calculation.

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