A long straight wire carrying current of 30 Amp is placed in an external uniform mag. field of i

step 1 Magnetic induction at a point from a straight conducting carrying current is given by B2 is equa

A long straight wire carrying current of 30 Amp is placed in...

A long straight wire carrying current of $30 \mathrm{Amp}$ is placed in an external uniform mag. field of induction $4 \times 10^{-4}$ tesla. The mag. field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2 \mathrm{~cm}$ away from the wire is tesla. (a) $10^{-4}$ (c) $5 \times 10^{-4}$ (b) $3 \times 10^{-4}$ (d) $6 \times 10^{-4}$

A long straight wire carrying current of $30 \mathrm{Amp}$ is placed in an external uniform mag. field of induction $4 \times 10^{-4}$ tesla. The mag. field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2 \mathrm{~cm}$ away from the wire is tesla.
(a) $10^{-4}$
(c) $5 \times 10^{-4}$
(b) $3 \times 10^{-4}$
(d) $6 \times 10^{-4}$

Key Concepts

Vector Addition of Magnetic Fields

When combining magnetic fields from different sources, it is important to consider both their magnitude and direction. In cases where the individual fields are perpendicular, the resultant field is found using the Pythagorean theorem. This method of vector addition is crucial for correctly determining the total magnetic field in a region.

Superposition Principle in Magnetism

This principle states that magnetic fields produced by different sources can be added together vectorially to determine the resultant magnetic field at any point. It is fundamental in electromagnetism because it allows the analysis of complex field configurations by breaking them down into simpler, individual contributions.

Magnetic Field Due to a Current-Carrying Conductor

A current-carrying conductor creates a magnetic field in the space around it. For a long straight wire, the magnetic field is given 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. This concept is central in understanding how currents produce magnetic effects according to the Biot–Savart law.

External Uniform Magnetic Field

An external uniform magnetic field has the same magnitude and direction at every point in a given region. Such fields are often used as a reference or background magnetic field, and they interact with other magnetic fields by vector addition, affecting the overall magnetic environment.

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