Two insulated wires of infinite length are lying mutually at...

Two insulated wires of infinite length are lying mutually at right angles to each other as shown in the figure. Current of $2 \mathrm{~A}$ and $1.5 \mathrm{~A}$ respectively are flowing in them. The value of magnetic induction at point $P$ will be (Figure can't copy) (a) $2 \times 10^{-3} \mathrm{~N} / \mathrm{A}-\mathrm{m}$ (b) $2 \times 10^{-5} \mathrm{~N} / \mathrm{A}-\mathrm{m}$ (c) Zero (d) $2 \times 10^{-4} \mathrm{~N} / \mathrm{A}-\mathrm{m}$

Two insulated wires of infinite length are lying mutually at right angles to each other as shown in the figure. Current of $2 \mathrm{~A}$ and $1.5 \mathrm{~A}$ respectively are flowing in them. The value of magnetic induction at point $P$ will be
(Figure can't copy)
(a) $2 \times 10^{-3} \mathrm{~N} / \mathrm{A}-\mathrm{m}$
(b) $2 \times 10^{-5} \mathrm{~N} / \mathrm{A}-\mathrm{m}$
(c) Zero
(d) $2 \times 10^{-4} \mathrm{~N} / \mathrm{A}-\mathrm{m}$

Key Concepts

Magnetic Field from a Straight Conductor

This concept involves understanding that a current-carrying wire produces a magnetic field in the surrounding space. The magnitude of the magnetic field produced by an infinitely long, straight wire is described by the formula B = ??I/(2?r), where ?? is the permeability of free space, I is the current, and r is the distance from the wire.

Superposition Principle

The superposition principle states that the net magnetic field at any given point due to multiple sources is the vector sum of the magnetic fields produced by each source individually. This principle is crucial when calculating the combined effect of magnetic fields from different wires or coils.

Right-Hand Rule

The right-hand rule is a technique used to determine the direction of the magnetic field generated by a current-carrying conductor. By pointing the thumb of the right hand in the direction of the current, the curl of the fingers indicates the circular direction in which the magnetic field lines circulate around the wire.

Vector Addition of Magnetic Fields

Since magnetic fields are vector quantities, they must be added using vector addition. When the fields from different current-carrying elements are perpendicular or have different directions, their combined effect is determined by adding the individual field vectors, taking into account both magnitude and direction.

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