Concepts Of Physics MCQ Edition [Volume 2]PhysicsMagnetic Field due to a Current
A long, straight wire of radius r carrying a uniformly distributed current i is positioned horizontally in a uniform magnetic field B that is directed vertically upward. What will be the minimum magnitude of the resultant magnetic field?
Options
- A0 if r ₀ i 2 B , and B - ₀ i 2 r if r < ₀ i 2 B
- B0 if r ₀ i 2 B , and B - ₀ i 2 r if r > ₀ i 2 B
- CB - ₀ i 2 r for all possible values of r
- D0 for all possible values of r
Correct answer
B. 0 if r ₀ i 2 B , and B - ₀ i 2 r if r > ₀ i 2 B
Step-by-step solution
The external magnetic field is B directed vertically upward. The magnetic field due to the current-carrying wire forms concentric circles. In the horizontal plane passing through the axis of the wire, the magnetic field is vertical. On one side of the wire, it is directed upward, and on the other side, it is directed downward. The resultant magnetic field will have a minimum magnitude on the side where the wire's magnetic field is directed downward, opposing the external field. The magnitude of the magnetic field d