Magnetic Force On A Current Carrying Wire

Step 1: Concept
A rotating charge constitutes a current . The magnetic moment is .
Step 2: Analysis
Current . Magnetic moment .
Step 3: Calculation
Torque . Since is vertical (along axis) and is horizontal, the angle is 90 . .
Step 4: Conclusion
Hence, the torque is .
Final Answer:(A)

When a conducting loop is moved through a magnetic field, the induced emf and the resulting current will generate forces on the segments of the wire. The forces are given by: Where is the induced current, is the length of the wire, and is the magnetic field strength. - acts on the side entering the magnetic field, with the least magnetic interaction. - and are the forces acting on the loop's sides where the magnetic field is strongest, as they are directly aligned with the field. - is the force acting on the side of the wire where the magnetic field is cutting through the loop the most efficiently. Therefore, the ranking is:

Step 1: Understanding the Concept:
This problem involves finding the direction of the magnetic force on a current-carrying conductor placed in a uniform magnetic field. The direction of this force is determined by the vector cross product of the current direction and the magnetic field direction, often visualized using the right-hand rule.

Step 2: Key Formula or Approach:
The magnetic force on a straight conductor of length carrying current in a uniform magnetic field is given by: The direction of the force is given by the direction of the cross product . We can use the Cartesian unit vectors ( for x, y, z axes respectively) to determine this direction.

Step 3: Detailed Explanation:
Given directions:
The current is in the z-direction. So, the direction of the length vector is along the z-axis, which can be represented by the unit vector .
The magnetic field is in the y-direction. So, the direction of is along the y-axis, represented by the unit vector .
Calculation of Direction:
The direction of the force is determined by the cross product .
Using the cyclic property of the cross product of unit vectors:


And the anti-cyclic property:


From this, we find that .
The vector represents the direction along the negative x-axis.

Step 4: Final Answer:
The magnetic force acting on the conductor is directed along the negative x-axis.