| |
|
|
| |
 |
| Numerical 07 |
|
| 07. A given length L of a uniform wire is bent (i) into a single circular turn and (ii) into n identical circular turns. What is the ratio of the magnetic field at the center of the coil in both the cases mentioned above when same current is passed through them? |
| |
| Suggested solution: |
| |
| Let r1 be the radius of the circular coil of one turn and B1 be the magnetic field at it's center due to current i. |
| |
| Then, |
| |
| 2 r1 = L or r1 = L/2 and B1 = monI / 2r1 = 2n2 moI / L |
| |
| Let r2 be the radius of each turn when the wire is bent into a circular coil having n turns. Also B2 is the magnetic field at the center due to the current I. |
| |
| Now, |
| |
| (2 r1) n = L or r1 = L/2n and B2 = mon I / 2r1 = 2 mon I / l |
| |
| From equations (1) and (2), we get |
| |
| B1 / B2 = 1/n |
| |
|
|
| |
|
|
| |
|
|
|
|
|
Moving Charges and Magnetism
|
|
|
