Concepts Of Physics MCQ Edition [Volume 2]PhysicsMagnetic Field due to a Current
An idealized magnetic field that is uniform within a specific region and abruptly drops to zero is sometimes depicted, as illustrated in the figure. By applying Ampere's law along the path PQRS , identify the reason why such a field configuration is impossible.
Options
- AAmpere's law is only applicable to non-uniform magnetic fields and cannot be evaluated along the chosen path.
- BThe line integral B d l over the loop PQRS is exactly zero, whereas the enclosed current is non-zero.
- CThe line integral B d l over the loop PQRS evaluates to a non-zero value, whereas the enclosed current is zero
- DThe line integral B d l is mathematically undefined at the boundary where the magnetic field abruptly drops to
Correct answer
C. The line integral B d l over the loop PQRS evaluates to a non-zero value, whereas the enclosed current is zero
Step-by-step solution
Consider the rectangular Amperian loop PQRS . The line integral of the magnetic field along the loop is given by: B d l = _P^Q B d l + _Q^R B d l + _R^S B d l + _S^P B d l Along the paths PQ and RS , the magnetic field B is perpendicular to the path elements d l , so B d l = 0 . Along the path QR , the magnetic field is zero, so _Q^R B d l = 0 . Along the path SP , the magnetic field B is uniform and parallel to d l . Let the length of SP be l . Then _S^P B d l = Bl . Therefore, the total line integral is B d l = B