How to Solve Ampere's Circuital Law Problem with Two Currents?

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In summary, the conversation is about finding the net magnetic field due to two straight long wires with currents i1 and i2 in the same direction. The formula for the general magnetic field due to a straight long current at point P is given as μ0i/2πr, where r is the perpendicular distance between the conductor and the point P. The steps to solve the problem are to find B1 and B2 due to the two wires, subtract them to get the net field, and integrate over a circle centered on the first wire. The question is then raised about how to eliminate i2 from the expression, to which the solution suggests that the contribution from the term with i2 should result in zero when integrated over the circle.
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shrabastee
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1. Homework Statement
In figure. (i1 and i2 are in the same direction. And the formula for field due to straight long wire is to be used.)


2. Homework Equations

General magnetic field due to a straight long current at point P=μ0i/2πr(r=perpendicular distance between the conductor and the point P)

3. The Attempt at a Solution

I just need some hints to work on. Please help!

EDIT:

These are the steps I came up with:
1)Find B1 due to conductor carrying i1
2)Find B2 due to conductor carrying i2(taking distance as (d-r))
3)Subtract the two to get net field.
4)Integrate.

But how do I eliminate the i2 from the expression??
 

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  • #2
the net field in each points indeed has i2 in it but when u integrate over a circle centered on the first wire, the contribution from the term that has i2 in it should result in zero
 
  • #3
Thanks! Are you sure my solution's right, though? Because this is a college problm and the solution I came up with seems a bit too simple. :P
 

FAQ: How to Solve Ampere's Circuital Law Problem with Two Currents?

What is Ampere's circuital law problem?

Ampere's circuital law problem is a mathematical principle that relates the magnetic field around a closed loop to the electric current passing through the loop. It states that the line integral of the magnetic field around a closed loop is equal to the permeability of free space times the total current passing through the loop.

How is Ampere's circuital law problem used in science?

Ampere's circuital law problem is used in many areas of science, particularly in electromagnetism and circuit analysis. It allows scientists to calculate the magnetic field around a current-carrying wire or a solenoid, and is also used to design and analyze electrical circuits.

What is the difference between Ampere's circuital law and Faraday's law?

Ampere's circuital law relates the magnetic field around a closed loop to the electric current passing through the loop, while Faraday's law relates the induced electromotive force (EMF) in a closed loop to the rate of change of magnetic flux through the loop. In simple terms, Ampere's law deals with the cause of magnetic fields, while Faraday's law deals with the effects of changing magnetic fields.

What are the limitations of Ampere's circuital law problem?

Ampere's circuital law problem is only valid for steady currents and does not take into account the effects of changing electric fields. It also assumes that the current is evenly distributed throughout the cross-section of the wire or loop. In certain situations, such as near a capacitor or in a rapidly changing circuit, Ampere's law may not give accurate results.

How is Ampere's circuital law problem related to Maxwell's equations?

Ampere's circuital law problem is one of the four Maxwell's equations, which are a set of fundamental equations that describe the behavior of electric and magnetic fields. Ampere's law is specifically related to the Maxwell-Ampere equation, which is a modified version of the original Ampere's law that takes into account the effects of changing electric fields.

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