Question

What is the magnetic field strength at points 2 to 4 in FIGURE EX29.1? Assume that the wires overlap closely at 2 and 3, that each point is the same distance from nearby wires, and that all other wires are too far away to contribute to the field.

Answer 1

It is provided that the wires overlap closely at points 2 and 3, point 2 and point 3 is same distance from nearby wires and other wires are faraway to contribute to the field. Therefore the magnetic field near the wire will be only due to the current flowing in the wire.

The magnetic field strength at point 2 in section of the wire is calculated as follows.

Consider the section at point 2.

$D:\Ani\G\719673-29-1E.png$

The current flowing through the wire causes magnetic field strength of. Point 2 is equidistant from segment and segment.

The current flowing through the wire produces magnetic field strength of 20 mT at any of its near points as provided in the question for point 1, .

Since the same current flowing through the wire segment and. Therefore, wire segment andalso produce the magnetic field of 20 mT at Point 3.

It can be noted that the current in section of the wire is moving in the same direction as it is moving in the section of the wire.

Hence the resultant magnetic field strength at point 2 is the sum of magnetic field strength due to segment and.

Therefore the magnetic field at point 2 is,

Hence, magnetic field strength at point 2 is.

The magnetic field strength at point 3 in section of the wire is calculated as follows.

Consider the section at point 3.

$D:\Ani\G\719673-29-1E.png$

The current flowing through the wire produces magnetic field strength of 20 mT at any of its near points as provided in the question for point 1, .

Point 3 is equidistant from segment and segment, as mentioned in question.

Since, the same current flowing through the wire segment and wire segment therefore the segment and segment produces the same magnetic field of 20 mT at Point 3.

It can be noted that the current in section of the wire is in opposite direction that of the current moving in the section of the wire.

Therefore, the resultant magnetic field strength at point 3 is the sum of magnetic field strength due to segment and.

Therefore the magnetic field at point 3 is,

Hence, magnetic field strength at point 3 is.

The magnetic field strength at point 4 in section of the wire is calculated as follows.

Consider the section at point 4.

$D:\Ani\G\719673-29-1E.png$

The current flowing through the wire produces magnetic field strength of 20 mT at any of its near points as provided in the question for point 1, .

Point 3 is equidistant from segment and segment, as mentioned in question.

Since, the same current flowing through the wire segment and wire segment therefore the segment and segment produces the same magnetic field of 20 mT at Point 3.

It can be noted that the current in section of the wire is flowing in the same direction that of the current flowing in the section of the wire.

Therefore, the resultant magnetic field strength at point 3 is the sum of magnetic field strength due to segment and.

Therefore the magnetic field at point 4 is,

Hence, magnetic field strength at point 4 is