Prove that magnetic field outside an infinite solenoid is equal to zero?

Question

Answer

Magnetic field outside a long solenoid can never be zero. Because a solenoid of finite length will have edges and field will come out. However, if we imagine a straigth solenoid of infonite length or a toroid, it will not have edges from where lines of force can come out.

Why is the magnetic field outside an ideal solenoid 0?

The magnetic field lines exist outside the solenoid, but the number of field lines per unit area outside the solenoid is much less compared to the number of lines per unit area inside the solenoid. Hence the magnetic field outside is so feeble that it is considered to be practically zero.

Answer

He.yy heres ur answer..Magnetic field outside a long solenoid can never be zero. Because a solenoid of finite length will have edges and field will come out. However, if we imagine a straigth solenoid of infonite length or a toroid, it will not have edges from where lines of force can come out.
Hope it helps!

Answer

Proof of zero magnetic field outside an infinite solenoid:
- Biot-Savart Law: According to the Biot-Savart Law, the magnetic field at a point due to a current-carrying wire is given by the cross product of the current element and the position vector divided by the distance squared.
- Magnetic field outside a solenoid: For an infinite solenoid, the magnetic field inside the solenoid is uniform and given by μ₀nI, where n is the number of turns per unit length and I is the current. However, outside the solenoid, the magnetic field is generally considered to be zero.
- Field cancellation: The reason for the magnetic field outside the solenoid being zero is that the magnetic field lines due to each turn of the coil cancel out the magnetic field lines due to the adjacent turns in such a way that the resultant magnetic field outside the solenoid is zero.
- Symmetry of the solenoid: Due to the symmetry of the solenoid, the magnetic field lines outside the solenoid cancel each other out in a way that the net magnetic field becomes zero.
- Infinite length: In the case of an infinite solenoid, the cancellation of magnetic field lines extends infinitely in all directions, resulting in a net magnetic field of zero outside the solenoid.
Therefore, due to the symmetry and infinite length of an infinite solenoid, the magnetic field outside the solenoid is equal to zero.

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