Magnetic Field due to long wire?

[Destroxia]

Homework Statement

In the figure, point P is at perpendicular distance R = 2.32 cm from a very long straight wire carrying a current. The magnetic field B set up at point P is due to contributions from all the identical current-length elements ids along the wire. What is the distance s to the element making (a) the greatest contribution to field B and (b)10.5% of the greatest contribution?

Homework Equations

Biot- Savart Law = u₀/4pi * (ids*sin(theta))/(r^2)

The Attempt at a Solution

I tried to set up an integration using the biot savart law and came up with something along the lines of,

u₀*i*R/(4pi) = ∫(-inf/inf) ds/(R^2+ s^2)^(3/2)

I solved (a) simply because I figured the strongest point of the magnetic field must be at the point closes to point P, the answer was 0, therefore.

I don't understand (b), if 0 is the greatest contribution, 10.5% of the greatest contribution would also be 0... Yet it is not.

 

[TSny]

OK for (a).

Let dB_max be the contribution from the current element that contributes the most. Part (b) is asking for the distance s for an element that contributes 10.5% of dB_max.

 

[Destroxia]

OK for (a).

Let dB_max be the contribution from the current element that contributes the most. Part (b) is asking for the distance s for an element that contributes 10.5% of dB_max.

So, essentially, I'm just finding the total B, taking 10.5% of that, and solving for the distance in the biot-savart law?

 

[TSny]

No, you do not need to find the total B. You are just comparing the contributions dB from individual segments (elements). In part (a) you considered the segment that produces the maximum dB. As you noted, this is the segment at s = 0. In (b) you want to find a segment that contributes a dB which is 10.5% of the amount contributed by the segment at s = 0.

 

[Destroxia]

No, you do not need to find the total B. You are just comparing the contributions dB from individual segments (elements). In part (a) you considered the segment that produces the maximum dB. As you noted, this is the segment at s = 0. In (b) you want to find a segment that contributes a dB which is 10.5% of the amount contributed by the segment at s = 0.

I guess I just meant, do I need to find the B at s = 0 then? If I don't, how would I find 10.5% of s = 0, If I don't know the value for that point?

 

[TSny]

You do not need to find a numerical value for the infinitesimal magnetic field, dB, produced at P by the element Ids located at s = 0. That would require knowing I and ds.

Think about the ratio of dB produced by two different current elements located at different values of s.