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Ampereâ€™s Circuital Law | Physics: Magnetic field due to the current carrying wire of infinite length using Ampereâ€™s law

Magnetic field due to the current carrying wire of infinite length using AmpÃ¨reâ€™s law

Consider a straight conductor of infinite length carrying current I and the direction ofmagnetic field lines is shown in Figure 3.42. Since the wire is geometrically cylindrical in shape and symmetrical about its axis, we construct an AmpÃ¨rian loop in the form of a circular shape at a distance *r* from the centre of the conductor as shown in Figure 3.42. From the AmpÃ¨reâ€™s law, we get

where is the line element along the amperian loop (tangent to the circular loop). Hence, the angle between magnetic field vector and line element is zero. Therefore,

where I is the current enclosed by the AmpÃ¨rian loop. Due to the symmetry, the magnitude of the magnetic field is uniform over the AmpÃ¨rian loop, we can take B out of the integration.

For a circular loop, the circumference is 2Ï€r, which implies,

In vector form, the magnetic field is

where *n* is the unit vector along the tangent to the AmpÃ¨rian loop as shown in the Figure 3.42. This perfectly agrees with the result obtained from Biot-Savartâ€™s law as given in equation (3.39).

EXAMPLE 3.18

Compute the magnitude of the magnetic field of a long, straight wire carrying a current of 1A at distance of 1m from it. Compare it with Earthâ€™s magnetic field.

Solution

Given that 1 = 1 A and radius r = 1 m

But the Earthâ€™s magnetic field is BEarth â‰ˆ 10âˆ’5 T

So, Bstraightwire is one hundred times smaller than BEarth.

Tags : Ampereâ€™s Circuital Law | Physics , 12th Physics : Magnetism and Magnetic Effects of Electric Current

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12th Physics : Magnetism and Magnetic Effects of Electric Current : Magnetic field due to the current carrying wire of infinite length using Ampereâ€™s law | Ampereâ€™s Circuital Law | Physics

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