What are the magnetic field strength and direction at points 1,2, and 3 in Figure P 24.6 ?

Name: Problem 6, Chapter 24: College Physics: A Strategic Approach
Uploaded: 2020-11-05T10:37:01-08:00
Duration: 9 min 28 s
Channel: Vishal Gupta
Description: What are the magnetic field strength and direction at points 1,2, and 3 in Figure P 24.6 ?

step 1 Hi, in the given problem, there are two current carrying conductors. The upper conductor is carr

What are the magnetic field strength and direction at points...

Key Concepts

Magnetic Field

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. It is characterized both by its strength (or magnitude) and its direction at any point in space. The concept is foundational in electromagnetism and is used to analyze how currents and magnetic materials interact.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field produced by a current-carrying conductor. By aligning the thumb of the right hand with the direction of the current, the curl of the fingers shows the circular direction of the resulting magnetic field around the conductor.

Biot-Savart Law

The Biot-Savart Law provides a quantitative method for calculating the magnetic field produced by a small segment of current. It states that the magnetic field contribution from a current element is proportional to the current and inversely proportional to the square of the distance from the element, and it emphasizes the vector nature of the field by including the sine of the angle between the current element and the position vector.

Ampère's Law

Ampère's Law relates the magnetic field circulating around a closed loop to the electric current passing through the loop. It is particularly useful for calculating the magnetic field in symmetric situations and provides a clear link between the current and the resulting magnetic field distribution.

Superposition Principle

The superposition principle in electromagnetism states that the total magnetic field created by multiple sources is the vector sum of the individual fields produced by each source. This principle is essential when calculating the net magnetic field at a point due to several current elements or conductors.

Transcript

00:01 Hi, in the given problem, there are two current carrying conductors.

00:08 The upper conductor is carrying a current of 10 ampere towards right and the lower conductor is carrying a current of 10 ampere but towards left.

00:28 There are three points.

00:32 Point number one, point 2 and point number 3.

00:40 This point number 1 is at a distance of 2 centimeter from the upper wire.

00:49 The total gap between the wires is 4 cm so.

00:56 This point number 2 is at a distance of 2 centimeter from the lower wire, from the upper wire as well as from the lower wire and this point number three is at a distance of two centimeter from the lower wire now we have to find the magnetic field the magnitude of magnetic field as well as the direction at all these three points so first of all at position one there are two magnetic fields one because of the upper wire and another because of the lower wire, b1 and b2.

01:51 And the net magnetic field at this point will be equal to the addition of these two fields.

02:03 Now, if you look for the direction of magnetic field due to the upper wire using right -hand thumb rule that will be upward, perpendicular to the plane of paper and the direction of magnet field due to the lower wire will be downward perpendicular to the plane of paper.

02:29 So the net magnetic field will become b1 minus b2 along with the sign convention.

02:39 So using vat and sever's law, the expression for b1 is mu not by 4 pi into 2 i1.

02:50 Divided by r1 minus mu not upon 4 pi 2 i2 divided by r2 this mu not by 4 pi can be taken out as a common here this 2 also will be same so taken out as a common now for i1 this is 10 ampere for r1 this is 2 centimeter or we can say this is 2 into 10 dash per minus 2 meter minus for i2 also 10 ampere and for r2 this is 4 plus 2 means 6 into 10 dashed power minus 2 meter then the value of this mu not upon 4 pi basis 10 r to power minus 7 tesla meter per ampere multiplied by 2 then this 10 ampier also taken as common out then remaining will be and in denominator 2 into 10 dash 1 minus 2 also comes out so the remaining in the bracket is 1 this is meter here 2 into 10 10x 1 minus 2 meter so remaining in the bracket is 1 minus 1 by 3 hence cancelling the similar units.

04:24 So this is meter and ampere and two.

04:31 So finally the answer for this net magnetic field at position 1 comes out to be 6 .7 into 10 dashed bar minus 5 s law which is in upward direction because the magnetic field in upward direction was more.

04:56 Then that in the downward direction.

04:59 Now we have to find the net magnetic field at position 2.

05:09 At this time the distance of this position 2 is 2 cm from both the wires...

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