Magnetic Field due to 2 Currents

[GeorgeCostanz]

Homework Statement

A current of 4.05 A is located 5.93 cm along the x axis, that is, at the point (5.93,0.00) cm. A current of 4.00 A is located 3.88 cm along the y axis, that is, at the point (0.00,3.88) cm. (These currents flow parallel to the z axis, with a positive current flowing in the + k direction.)

Find the magnetic field at the origin.

Enter the x and y components of the field:

Homework Equations

ampere's law

The Attempt at a Solution

i kno i have to use ampere's law, but I'm not sure how to do this with 2 currents

i attempted to find each current's magnetic field and then added the x and y components of each together

i drew a diagram but this RH rule stuff goes completely over my head
not sure if i have to use an angle somewhere or what

 

[anathema]

Thank you for your question. To find the magnetic field at the origin, we can use the superposition principle, which states that the total magnetic field at a point is equal to the vector sum of the individual magnetic fields produced by each current. In this case, we have two currents, one along the x-axis and one along the y-axis.

To find the magnetic field at the origin, we can use the following steps:

1. Calculate the magnetic field produced by the current along the x-axis at the origin. We can use the formula B = μ0I/2πr, where μ0 is the permeability of free space, I is the current, and r is the distance from the current to the point of interest. In this case, r = 5.93 cm. This will give us the x-component of the magnetic field.

2. Calculate the magnetic field produced by the current along the y-axis at the origin. Again, we can use the formula B = μ0I/2πr, but this time, r = 3.88 cm. This will give us the y-component of the magnetic field.

3. Add the x and y components together to find the total magnetic field at the origin.

It is important to note that since the currents are parallel to the z-axis, the magnetic field produced by each current will be perpendicular to the x-y plane. This means that the x and y components of the magnetic field will be equal and opposite, resulting in a net magnetic field of 0 at the origin.

I hope this helps! If you have any further questions, please let me know.



Scientist