Calculating Magnetic Field of a Tight Coil

[lemaire]

Homework Statement

A 1.88 m long wire carrying 3.1 A is wound into a tight, loop shaped coil 0.05 cm in diameter. What is the magnetic field at its center?

Homework Equations

The Attempt at a Solution

I use Ampere's law but i get the wrong answer. I think i did not set up the equation right. Please i need answer with equation so i can compare it to mine not a chat.
Thank you for your comprehension.

 

[berkeman]

Post the work that you did, and then we can try to help you. We do not give out answers here on the PF (check the Rules link at the top of the page).

What equations are you using? I'm also moving this thread to Intro Physics.

 

[baba89]

Dear student,

Thank you for reaching out for assistance with your homework problem. As a scientist, my goal is to guide and support your understanding of the concepts and equations involved in solving this problem, rather than simply providing you with the answer. I will do my best to explain the steps involved in solving this problem and provide you with the necessary equations.

To calculate the magnetic field at the center of a tight coil, we can use the equation B = μ0nI, where B is the magnetic field, μ0 is the permeability constant (4π x 10^-7 Tm/A), n is the number of turns per unit length, and I is the current.

In this problem, we are given the length of the wire (1.88 m), the current (3.1 A), and the diameter of the coil (0.05 cm). We can calculate the number of turns per unit length by dividing the total length of the wire by the circumference of the coil. The circumference can be calculated using the formula C = πd, where d is the diameter of the coil.

Therefore, the number of turns per unit length is n = 1.88 m / (π x 0.05 cm) = 119.4 turns/m. Now, we can plug in all the values into the equation B = μ0nI to calculate the magnetic field at the center of the coil.

B = (4π x 10^-7 Tm/A) x (119.4 turns/m) x (3.1 A) = 1.47 x 10^-4 T

I hope this helps you understand the correct approach to solving this problem. If you have any further questions or need clarification on any of the steps, please do not hesitate to ask. Remember, as a scientist, it is important to not just rely on the answer, but to understand the process and equations involved in solving a problem. Keep up the good work!