A positive charge q is distributed over a circular ring of radius a. It is placed in a horizontal plane and is rotated about its axis at a uniform angular speed . A horizontal magnetic field B exists in the space. The torque acting on the ring due to the magnetic force is ________.
1
2
3
4
Official Solution
Correct Option: (1)
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)
02
PYQ 2023
medium
physicsID: cuet-ug-
A square loop of copper wire is pulled through a region of uniform magnetic field as shown. Rank the pulling forces , , , and that must be applied to keep the loop moving with constant speed ( ):
1
2
3
4
Official Solution
Correct Option: (2)
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:
03
PYQ 2025
easy
physicsID: cuet-ug-
A conductor is placed along z-axis carrying current in z direction in uniform magnetic field directed along y-axis. The magnetic force acting on the conductor is directed along:
1
positive x-axis
2
positive y-axis
3
positive z-axis
4
negative x-axis
Official Solution
Correct Option: (4)
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.
