A long straight wire carries 20 A along the xaxis Part A Fin

A long straight wire carries 2.0 A along the +x-axis.

Part A

Find the magnitude of the magnetic field at a point 18 cm away on the +y-axis.

Express your answer to two significant figures and include the appropriate units.

Part B

Find the direction of the magnetic field at a point 18 cm away on the +y-axis.

Find the direction of the magnetic field at a point 18  away on the -axis.

Part C

Find the magnitude of the magnetic field at a point 18 cm away on the y-axis.

Express your answer to two significant figures and include the appropriate units.

Part D

Find the direction of the magnetic field at a point 18 cm away on the y-axis.

Find the direction of the magnetic field at a point 18  away on the -axis.

Solution

For a very long wire carrying current as I, the magnetic field at a given distance, say a, can be obtained by Ampere\'s law and is given as

B = oI/ 2 a

Now, as per the relation above, the magnitude depends only on the distance from the wire. Hence for all the parts of the question, the magnitude will remain same if the distance from the wire under consideration is same.

Part A: The magnitude of the magnetic field at distance of 18 cm will be given as:

B = 4x 10^-7 x 2 / 2 x 0.18 = 22.222 x 10^-7 T

Part B: The direction of the magnetic field due to a wire can be determined by the right hand rule. We need to curl our fingers around the wire with the thumb pointing towards the direction of the current. At any point, the direction of the turn of the fingers give the direction of the magnetic field.

Using the above rule, we get that the direction of the field at a point on +y axis would be along the perpendicular on xy plane. That is, the direction of field would be along + z axis.

For a point on - Yaxis, the curl of fingers would be downwards, hence the direction would -z axis.

Part C: For a point at a distance of 18 cm along the -Y axis, the magnitude of distance is same as PartA, hence the magnitude of the magnetic field would be:

B = 22.222 x 10^-7 T

Part D: As mentioned above, the direction of the curl of fingers for a point on -Y axis would be going downwards. Hence the direction of field would be along -Z axis.