Calculating Magnetic Field of a Toroid Using Ampere's Law

[snipaj9696]

Use ampere's law to determine the magnetic field (a) inside and (b) outside a toroid, which is like a solenoid bent into the shape of a circle.

Here is my work..

IS MY WORK CORRECT?

a.) B(2PIr)=MoIenc

and I found that B=MoNI/2pir


b.) the magnetic field is 0 outside the loop

 

[Hootenanny]

Yes, you are correct.

For future reference we have Homework forums, for such questions where your query may receive more attention.

 

[Moetasim]

.

Your work appears to be correct. Ampere's law states that the magnetic field around a closed loop is proportional to the current passing through the loop. In the case of a toroid, where the current is confined to the inside of the loop, the magnetic field outside the loop will be zero. This is because the magnetic field lines created by the current in one part of the loop will cancel out the field lines created by the current in another part of the loop. However, inside the loop, the magnetic field will be non-zero and can be calculated using the formula you provided. It is important to note that this calculation assumes a perfect toroid with no external magnetic fields present. Any external fields would need to be taken into account in the calculation. Overall, your understanding and application of Ampere's law in this scenario is accurate.