# Magnetic Fields due to currents

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The magnetic flux density at a distance d from the current carrying wire is given by:

$B = \frac{\mu_{o} I }{2 \pi d}$, where

• $I$ is the current through the wire,
• d is the distance away from wire
• $\mu_{o}$ is the permeability of free space.

The magnetic flux lines would be further apart when r increases as the magnetic field gets weaker further away from the wire.

Right hand grip rule:

Diagram by Jfmelero, Link: http://en.wikipedia.org/wiki/File:Manoderecha.svg, available under Creative Commons Attribution-Share Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license.

When a straight wire is bent into a loop(a circular coil), the magnetic field is concentrated in the centre.

• Field pattern is symmetrical about the coil
• Direction of the field can be obtained by using a modified version of right hand grip rule (Corkscrew rule). The fingers curl in direction of the conventional current. The thumb will then point in the direction of the field.

Equation for magnetic flux density at the centre of the coil:

$B = \frac{\mu_{o} N I}{2r}$, where

• $I$ is current through the coil
• N is the number of loops in the coil
• r is the radius of the coil.

Solenoid:

• A solenoid produces a magnetic field similar to that of a permanent bar magnet.
• The magnetic field within a solenoid is very nearly uniform
• The direction of the magnetic field can be obtained by the Corkscrew rule
• The magnetic flux density at the ends of a solenoid is half that at the centre

Magnetic flux density at centre of solenoid:

$B = \mu_{o} n I$, where

• $I$ is current through coil
• n is number of turns per unit length

Force between two straight, parallel current carrying wires.

• Force per unit length on each wire is given by: $\frac{F}{l} = \frac{mu_{o} I_{1} I_{2}}{2 \pi d}$
• When the currents flow in the same direction, there is an attractive force between them.
• When the currents flow in opposite directions, there is a repulsive force between them.

A good explanation for the above can be found here: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/wirfor.html.

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