Calculate Magnetic Field from Current on a Loop of Wire

In summary, a single loop of wire with a radius of 3 cm and carrying a current of 2.4 A produces a magnetic field with a magnitude of 4.2357797e-4 T at a position 1 cm from the center of the loop. This can be calculated using the equation B = (μ0)*(I)/(2*R). Further calculations for other positions (b, c, d) are still needed.
  • #1
fball558
147
0
magnetic field ??

Homework Statement



A single loop of wire of radius 3 cm carries a current of 2.4 A. What is the magnitude of B on the axis of the loop at the following position?
1 cm from the center



Homework Equations



Uo/4(pi) * (2(pi)R^2 *I) / (z^2 + R^2)^(3/2)

where Uo is 4(pi) X 10^-7

The Attempt at a Solution



i just pluged in values
R = .03 m
z = .01 m
I = 2.4 A

i got 4.2357797e-4 T but that is wrong??
does anyone see something that I am doing wrong?
any help would be great!
 
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  • #2


for x = 0 (at center of loop)

B = (μ0)*(I)/(2*R)

don't know how to get b, c, or d yet though.
 
  • #3


Your attempt at a solution is correct. The only error is in the units. The magnetic field is in Tesla (T), not microTesla (uT). Therefore, the correct answer is 0.00042358 T.
 

1. How do I calculate the magnetic field from a current on a loop of wire?

To calculate the magnetic field from a current on a loop of wire, you can use the formula:

B = (μ0 * I * N) / (2 * R), where B is the magnetic field, μ0 is the permeability of free space, I is the current, N is the number of turns in the loop, and R is the radius of the loop.

2. What is the direction of the magnetic field from a current on a loop of wire?

The direction of the magnetic field is determined by the right-hand rule. If you point your thumb in the direction of the current, the direction of your fingers curling around the loop will indicate the direction of the magnetic field.

3. How does the magnetic field change if the current or loop size is altered?

The magnetic field is directly proportional to the current and the number of turns in the loop, and inversely proportional to the radius of the loop. This means that if the current or number of turns is increased, the magnetic field will also increase. If the radius is increased, the magnetic field will decrease.

4. Can the magnetic field be calculated at any point in space?

Yes, the magnetic field can be calculated at any point in space using the formula B = (μ0 * I * N * sinθ) / (2 * r), where θ is the angle between the direction of the current and the line connecting the point to the center of the loop, and r is the distance from the center of the loop to the point.

5. How is the magnetic field affected by the shape of the loop?

The shape of the loop does not affect the magnitude of the magnetic field, but it can affect the direction and distribution of the field. If the loop is not circular, the direction of the magnetic field may not be uniform along the loop's perimeter. Additionally, if the loop is not flat, the field may also vary in strength along its height.

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