Magnetic field of circular loop

[Qaztgbe]

Homework Statement

Two small identical circular loops carrying equal currents are placed with the geometrical axis perpendicular to each other. Find the magnitude and direction at a point O at an equal distance x from their centers.

Homework Equations

Magnetic field of a current carrying circular loop at a distance x on it's axis : μIR²/2x³ when x>>>R

The Attempt at a Solution

Let μIR²/2x³ = B
Then magnitude should be (2^1/2)B(Fields perpendicular to each other)
Inclined at an angle 45° with the horizontal.

Are my directions right?

 

[DukeLuke]

Your equation for the magnetic field seems like it's missing a factor of 2 in the denominator. Also, check your vector addition when adding the magnitudes of the fields.

 

[SammyS]

Directions look right, although, it's hard for the viewer to be certain of the direction of current flow.

B^1/2 is not correct. That's the square root of B.

 

[Qaztgbe]

!
Sorry about that. I meant, (2^1/2)B (I don't know how to make the squareroot symbol here) And yes, the equation was missing a 2. Typo again.
I don't have any problems with the magnitude. Just the direction. The solution in my book has a direction opposite to the one I got.

 

[rwisz]

Your directions are not quite right. The correct directions would be:

- The magnitude of the magnetic field at point O is given by B = μIR^2 / 2x^3, where R is the radius of the circular loops and x is the distance from their centers.
- The direction of the magnetic field at point O would depend on the direction of the currents in the loops. If the currents are in the same direction, the magnetic field would be pointing out of the page (perpendicular to the plane of the loops). If the currents are in opposite directions, the magnetic field would be pointing into the page (perpendicular to the plane of the loops).
- The magnetic fields from the two loops would combine at point O, resulting in a net magnetic field that is inclined at an angle of 45° with the horizontal.