Calculating Magnetic Field with Helmholtz Coils

In summary, the conversation is about a set of Helmholtz coils with 186 turns and a radius of 15.9 cm, with a current of 2.2 A. Part a) involves calculating the magnetic field at the center of the two coils when the current is going in the same direction, while part b) asks for the magnetic field at the center when the currents are going in opposite directions. The formula B= (KN/R) *I is used for part a), but the solution for part b) is still unclear.
  • #1
sheri1987
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0

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?
 
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  • #2
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...
 
  • #3


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!
 

1. What are Helmholtz coils?

Helmholtz coils are a pair of identical circular or square-shaped electromagnets placed parallel to each other and equidistant from each other. They are used to generate a uniform and steady magnetic field.

2. How do Helmholtz coils calculate magnetic fields?

Helmholtz coils use the Biot-Savart law, which states that the magnetic field at a point is directly proportional to the current flowing through the conductor and inversely proportional to the distance from the conductor. By using two identical coils with opposite currents, a uniform magnetic field can be created at the center point between them.

3. What factors affect the strength of the magnetic field produced by Helmholtz coils?

The strength of the magnetic field produced by Helmholtz coils is affected by the current flowing through the coils, the distance between the coils, and the number of turns in the coils. The larger the current, the closer the coils are together, and the more turns in the coils, the stronger the magnetic field will be.

4. How is the direction of the magnetic field determined in Helmholtz coils?

The direction of the magnetic field produced by Helmholtz coils is determined by the right-hand rule. If the fingers of the right hand wrap around the coils in the direction of the current, the thumb will point in the direction of the magnetic field.

5. What is the practical application of calculating magnetic field with Helmholtz coils?

Helmholtz coils are commonly used in scientific research, particularly in studies of magnetism and electromagnetism. They are also used in industries such as electronics, where a uniform magnetic field is needed for testing and calibration purposes.

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