Question

$\pi $ ampere current is flowing through a long straight wire. Due to this field of \[5\times {10^{ - 5}}T\]produced, then distance of the point from the axis of wire is:
A. ${10^4}{\mu _o}m$
B. ${10^5}{\mu _o}m$
C. ${10^6}{\mu _o}m$
D. ${10^8}{\mu _o}m$

Answer 1

Hint: When the current starts flowing through this long straight conductor, the magnetic field is generated around the long straight wire and when current flowing through wire is stopped, the magnetic field generated around wire vanishes.

Complete step by step solution:
Given: Magnetic field = \[5 \times {10^{ - 5}}T\]
Current $(i) = \pi $
The long straight wire is carrying current through it. The length of wire is not mentioned. Hence we will assume it may have infinity length.
Permeability of air =${\mu _{_o}}$
And permeability of air equals to \[1.25663753 \times {10^ - }^6\]i.e $4\pi \times {10^{ - 7}}$
Whereas permeability of free space is $1$.
Current in the straight wire =$\;I{\text{ }} = \pi $
According to the ampere, a magnetic field is created at whatever point an electrical charge is moving. The turning and circling of the core of a particle delivers an attractive field as doe’s electrical flow moving through a wire. The bearing of the turn and circle decide the course of the attractive field.
When the current starts flowing through this long straight conductor, the magnetic field is generated around the long straight wire and when current flowing through wire is stopped, the magnetic field generated around the wire vanishes.
 Here the magnetic field generated = \[5 \times {10^{ - 5}}T\]
Therefore, magnetic field around the wire can be given by the formula:
$B = \dfrac{{{\mu _o}i}}{{2\pi d}}$
Where $d$ = distance of the point from the axis of wire
$5 \times {10^{ - 5}} = \dfrac{{4\pi \times {{10}^ - }^7 \times \pi }}{{2\pi d}}$
$\therefore d = \dfrac{{2\pi \times {{10}^{ - 7}}}}{{5 \times {{10}^{ - 5}}}}$
$\therefore d = 0.4\pi \times {10^{ - 3}}$
Therefore, distance of the point from the axis of wire = $4\pi \times {10^{ - 4}}m$

Hence option (A) is the correct answer.

Note: Basically, magnetic field is the area around the magnet in which the effect of magnetic force can be experienced. If any current carrying conductor is there, it will experience some magnetic field and the direction of magnetic field along the long straight wire can be given by Right hand thumb rule. According to the right hand thumb rule, the thumb will represent the direction of current and curling of fingers of the right hand will represent the direction of the magnetic field. Depending on the shape of the conductor, the contour of the magnetic field will vary.