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

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To solve Ampere's Circuital Law problem involving two currents, the magnetic field contributions from each wire need to be calculated separately using the formula for a long straight wire. The first step involves determining the magnetic field B1 from the wire carrying current i1, followed by calculating B2 from the wire carrying current i2, adjusting for distance. The next step is to find the net magnetic field by subtracting B2 from B1 and integrating over a specified area. A key challenge is eliminating the influence of i2 during integration, as its contribution should ideally cancel out when centered around the first wire. The solution appears straightforward, but concerns about its simplicity in a college-level context are noted.
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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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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
 
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
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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