Calculating Magnetic Field with Helmholtz Coils

[sheri1987]

Homework Statement

The coils in a set of Helmholtz coils have 186 turns and a radius of 15.9 cm. The current is set at 2.2 A. Express your answers in units of "T" for Tesla.

a) Calculate the magnetic field along the axis at the center of the two coils (x = 0).

b) What is the magnetic field at the center if the currents in the two coils are going in opposite directions?

Homework Equations

B= (KN/R) *I <-----used for part A

The Attempt at a Solution

I obtained the correct answer of .0023 Tesla for part a); however, I am unsure how to do part b) ...any help?

 

[phyzmatix]

If the current flows in opposite directions, the induced magnetic fields will be directed away from each other wouldn't they? I'm no expert at coils, but I'd look at the possibility of treating the two halves separately...

 

[baba89]

I would like to first commend you on obtaining the correct answer for part a) using the formula B= (KN/R) *I. This formula is commonly used to calculate the magnetic field for Helmholtz coils and it is great that you were able to apply it correctly in this scenario.

To answer part b), we need to consider the effect of the currents in the two coils being in opposite directions. In this case, the magnetic fields created by each coil will cancel each other out. This is because the magnetic field created by a circular current-carrying loop is perpendicular to the plane of the loop, and in opposite directions for opposite currents.

Therefore, at the center of the two coils, the magnetic field would be zero if the currents are going in opposite directions. This can also be confirmed by plugging in the values into the formula B= (KN/R) *I, where the currents would be negative for one of the coils, resulting in a net magnetic field of zero at the center.

I hope this helps clarify your understanding of Helmholtz coils and their magnetic fields. Keep up the good work in your studies of electromagnetism!