The figure below shows two current carrying wires and the directions of the currents they carry. The wires carry the following currents: I1 = 7.1 A and I2 = 8.9 A. Wire 1 is at (0, 5.8) mm; wire 2 is at (15.1, 0) mm; point P is at (15.1, 5.8) mm. Wire 1 is pointing into the page, and wire 2 is pointing out of the page.


What are the magnitude and direction (measured with respect to the +x direction) of the total magnetic field due to the two wires at point P?

I used the equation B = (µoI)/(2ðR) to solve for each vector. Wire 1 produces a downward magnetic field on point P, and wire 2 produces a leftward magnetic field on point P. Then, I used the pythagorean theorem to solve for the net magnetic field. I found the net magnetic field to be 3.21E-4 T and the direction to be 17.02 degrees, but this answer is incorrect. What am I doing wrong?

In order to correctly calculate the net magnetic field at point P, you need to consider the direction of the magnetic field produced by each wire as well as the vector sum of the individual magnetic fields.

Here's a step-by-step guide to calculating the net magnetic field at point P:

1. Determine the distance between each wire and point P:
- For Wire 1: The distance between Wire 1 and P is given by the y-coordinate of P (5.8 mm).
- For Wire 2: The distance between Wire 2 and P is given by the x-coordinate of P (15.1 mm).

2. Determine the magnetic field contributed by each wire at point P using the formula:
B1 = (µo × I1)/(2π × R1) (Wire 1)
B2 = (µo × I2)/(2π × R2) (Wire 2)
where µo is the permeability of free space (4π × 10^(-7) T·m/A), I1 and I2 are the currents in Wire 1 and Wire 2 respectively, R1 and R2 are the distances from Wire 1 and Wire 2 respectively to point P.

3. Calculate the x-component and y-component of the magnetic field contributed by each wire at point P:
B1x = 0 (Wire 1 is pointing into the page, so it only contributes to the y-component of the magnetic field)
B1y = B1 (Wire 1 contributes to the y-component of the magnetic field)
B2x = B2 (Wire 2 contributes to the x-component of the magnetic field)
B2y = 0 (Wire 2 is pointing out of the page, so it only contributes to the x-component of the magnetic field)

4. Find the net magnetic field at point P by summing the x-components and y-components from each wire:
Bx = B1x + B2x
By = B1y + B2y

5. Finally, calculate the magnitude and direction (measured with respect to the +x direction) of the total magnetic field at point P using the x-component and y-component:
B = √(Bx^2 + By^2)
Direction = tan^(-1)(By/Bx)

By following these steps, you should be able to obtain the correct values for the magnitude and direction of the total magnetic field at point P.

To determine the magnitude and direction of the total magnetic field at point P, you correctly used the formula B = (µ0I)/(2πR) to calculate the magnetic fields produced by each wire. However, the error in your solution lies in determining the direction of the magnetic fields produced by the wires.

When calculating the direction of the magnetic field, you need to consider the right-hand rule. Imagine holding your right hand so that your thumb points in the direction of the current in the wire. Your curled fingers will indicate the direction of the magnetic field. Here's the important part: when both wires are in the same plane, the direction of the magnetic field produced by each wire depends on the relative position of the wires and the point where you are calculating the field.

In this case, wire 1 is pointing into the page, and wire 2 is pointing out of the page. The direction of the magnetic field produced by each wire at point P can be determined as follows:

1. Wire 1: Since wire 1 is located above point P, the magnetic field produced by it can be directed to the left.

2. Wire 2: Wire 2 is located to the right of point P. Following the right-hand rule, the magnetic field produced by wire 2 will be directed into the page.

To find the net magnetic field at point P, you need to consider the vector sum of the individual magnetic fields. Given that wire 1 produces a magnetic field directed to the left and wire 2 produces a magnetic field directed into the page, the net magnetic field will be the vector sum of these two fields.

To calculate the magnitude of the net magnetic field, you can use the Pythagorean theorem as you did before. You just need to make sure you are adding the magnitudes of the individual magnetic fields correctly.

However, the direction of the net magnetic field is not directly obtained from the Pythagorean theorem. Instead, you need to use trigonometry to find the angle between the resultant magnetic field and the positive x-axis.

Once you recalculate the individual magnetic fields and correctly consider their directions, you should be able to find the correct magnitude and direction of the net magnetic field at point P.

First of all, thank you for showing your work. So few of the students do, despite out pleading. Thank you also for clearly describing the Figure that could not be shown.

It seems you went about the problem in the right way. The fields due to the two different wires at P are perpendicular, so the Pythagorean theorem should give the resultant.

I also abree with your individual B field directions, using the right hand rule.

The equation
B = (µo*I)/(2*pi*R)
is correct for the individual field contributions of each wire. Did you convert the distances R to meters?

I used that equation to solve for the contributions from each wire. I accidently used the equation for magnetic field for a loop (instead of this wire equation) the first time I submitted the homework problem. The angle was incorrect the first time I submitted it too, but it is the same even after I corrected my error. I used the magnetic field components to solve for the angle. I did tan(theta) = B1/B2 to solve for the angle of the net magnetic field above the x axis. I must be doing that part wrong. Thank you very much for your help.