Concepts Of Physics MCQ Edition [Volume 2]PhysicsMagnetic Field
A circular wire-loop of radius a and carrying a current i is placed in a perpendicular magnetic field B , as shown in the figure. Assume the radius of the wire's cross section is r . Determine the increase in the radius of the loop when the magnetic field is switched off. The Young modulus of the wire's material is Y .
Options
- Ai a^2 B r^2 Y
- Bi a B r^2 Y
- Ci a^2 B 2 r^2 Y
- D2 i a^2 B r^2 Y
Correct answer
A. i a^2 B r^2 Y
Step-by-step solution
Consider a small element of the circular wire-loop subtending an angle d at the center. The length of this element is dl = a d . The magnetic force acting on this small element is given by: dF = i dl B = i (a d ) B According to the right-hand rule (or Fleming's left-hand rule), since the current is counter-clockwise and the magnetic field is directed into the page, the magnetic force on each element is directed radially inward. This inward force compresses the loop. To maintain equilibrium, a compressive force (ten