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I'm just studying past exams for my physics exam in a few days.

I've been struggling with this question

http://img823.imageshack.us/img823/7469/45633341.jpg [Broken]

The first thing i did was use the Biot-Savart law to find the magnetic field at z=0, or at ±d/2 away from z=0

I found the field for each loop seperately and since the bottom loop was orientated in the opposite direction to the above loop it was the negative of the above field. Since the dl' vector faced the opposite way when observing from z=0,

So then when i added the two fields together ofcourse they cancelled but theres no way this is right,

It says to find the derivative of B wrt z AT z=0, my equation doesnt have z in it as i found the field a distance z = ±d/2, so I suppose I could change the d/2 to z, but ill at z=0 they will still cancel get B=0 at that point so the derivative would also be zero.

In the last part it asks for the second derivative of z, with a new d, so this makes it clear my equation is wrong, haha, because mine either has d OR z

The equation i found using biot-savart for the top loop was,

B(d/2) = [itex]\frac{μIR^{2}}{2(R^{2}+\frac{d^{2}}{4})^{3/2}}[/itex]

and the bottom was just negative it

Should I be trying to find the field at an arbitrary z? If i do that, and z>d/2 then will the field be the field in the z direction of the bottom loop plus the field due to the top loop? and in the equation for the bottom loop the distance vector will have an extra d term right?

Is there an easier method I'm not seeing?

Thanks in advanced

I've been struggling with this question

http://img823.imageshack.us/img823/7469/45633341.jpg [Broken]

The first thing i did was use the Biot-Savart law to find the magnetic field at z=0, or at ±d/2 away from z=0

I found the field for each loop seperately and since the bottom loop was orientated in the opposite direction to the above loop it was the negative of the above field. Since the dl' vector faced the opposite way when observing from z=0,

So then when i added the two fields together ofcourse they cancelled but theres no way this is right,

It says to find the derivative of B wrt z AT z=0, my equation doesnt have z in it as i found the field a distance z = ±d/2, so I suppose I could change the d/2 to z, but ill at z=0 they will still cancel get B=0 at that point so the derivative would also be zero.

In the last part it asks for the second derivative of z, with a new d, so this makes it clear my equation is wrong, haha, because mine either has d OR z

The equation i found using biot-savart for the top loop was,

B(d/2) = [itex]\frac{μIR^{2}}{2(R^{2}+\frac{d^{2}}{4})^{3/2}}[/itex]

and the bottom was just negative it

Should I be trying to find the field at an arbitrary z? If i do that, and z>d/2 then will the field be the field in the z direction of the bottom loop plus the field due to the top loop? and in the equation for the bottom loop the distance vector will have an extra d term right?

Is there an easier method I'm not seeing?

Thanks in advanced

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