The magnetic induction at a point P which is at a distance 4 cm from a long current carrying wi

Name: Problem 1868, Chapter 13: JEE Physics
Uploaded: 2021-10-02T09:17:23-08:00
Duration: 1 min 1 s
Channel: Narayan Hari
Description: The magnetic induction at a point P which is at a distance 4 cm from a long current carrying wire is 10^-8 tesla. The field of induction at a distance 12 cm from the same current would be tesla. (a) 3.33 ×10^-9 (b) 1.11 ×10^-4 (c) 3 ×10^-3 (d) 9 ×10^-2

step 1 As we know that B is inversely proportional to R. I can write the value of B1 by B2 is equal to

Question

The magnetic induction at a point $P$ which is at a distance $4 \mathrm{~cm}$ from a long current carrying wire is $10^{-8}$ tesla. The field of induction at a distance $12 \mathrm{~cm}$ from the same current would be tesla. (a) $3.33 \times 10^{-9}$ (b) $1.11 \times 10^{-4}$ (c) $3 \times 10^{-3}$ (d) $9 \times 10^{-2}$

   The magnetic induction at a point $P$ which is at a distance $4 \mathrm{~cm}$ from a long current carrying wire is $10^{-8}$ tesla. The field of induction at a distance $12 \mathrm{~cm}$ from the same current would be tesla.
(a) $3.33 \times 10^{-9}$
(b) $1.11 \times 10^{-4}$
(c) $3 \times 10^{-3}$
(d) $9 \times 10^{-2}$

JEE Physics

StemEZ 1st Edition

Chapter 13, Problem 1868

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Solved by Expert Narayan Hari

10/02/2021

Step 1

Step 1: The magnetic field induction $B$ due to a long current carrying wire at a distance $r$ from the wire is given by the formula $B = \frac{\mu I}{2\pi r}$, where $\mu$ is the permeability of free space, $I$ is the current in the wire, and $r$ is the distance Show more…

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The magnetic induction at a point $P$ which is at a distance $4 \mathrm{~cm}$ from a long current carrying wire is $10^{-8}$ tesla. The field of induction at a distance $12 \mathrm{~cm}$ from the same current would be tesla. (a) $3.33 \times 10^{-9}$ (b) $1.11 \times 10^{-4}$ (c) $3 \times 10^{-3}$ (d) $9 \times 10^{-2}$

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Key Concepts

Magnetic Field due to a Current-Carrying Wire

This concept involves the understanding that a long, straight conductor with an electric current produces a magnetic field in the surrounding space. The magnetic field around such a wire is given by the formula B = ??I/(2?r), where ?? is the permeability of free space, I is the current, and r is the radial distance from the wire. This relationship is a fundamental aspect of electromagnetism and is derived using Ampere's law.

Inverse Proportionality with Distance

The magnetic field created by a current-carrying wire is inversely proportional to the distance from the wire. This means that as the distance increases, the strength of the magnetic field decreases by the same factor. This concept allows the determination of the magnetic field at different distances by scaling, which is crucial for solving problems involving magnetic fields around conductors.

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