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. Determine the locations where the resultant magnetic field attains its maximum magnitude, and find this maximum magnitude.
Options
- ALooking along the direction of current, at the leftmost points on the wire's surface; B + ₀ i 2 r
- BAt points lying on the central axis of the wire; B + ₀ i 2 r
- CLooking along the direction of current, at the topmost points on the wire's surface; B^2 + ( ₀ i 2 r )^2
- DLooking along the direction of current, at the rightmost points on the wire's surface; B + ₀ i 2 r
Correct answer
A. Looking along the direction of current, at the leftmost points on the wire's surface; B + ₀ i 2 r
Step-by-step solution
Let the observer look along the direction of the current, meaning the current is flowing away from the observer into the plane. According to the right-hand grip rule, the magnetic field lines produced by the straight wire form concentric clockwise circles around the wire. The external uniform magnetic field is directed vertically upward. To obtain the maximum resultant magnetic field, the magnetic field produced by the wire must be in the same direction as the external magnetic field (i.e., vertically upward). Look