Magnetic Force

Step 1: Concept
.
Step 2: Analysis
Given . .
Step 3: Conclusion
.
Final Answer: (C)

Step 1: Formula
The spin-only magnetic moment is given by BM, where is the number of unpaired electrons.
Step 2: Calculation
Given , so . Squaring both sides: .
Step 3: Solve for n
. Since must be positive, .
Final Answer: (a)

Step 1: Formula for radius of motion of electron.
The radius of the electron's circular path in the magnetic field is given by: where is the mass of the electron, is the velocity of the electron, is the charge of the electron, and is the magnetic field strength. The diameter is simply twice the radius:

Step 2: Use given data and solve.
From the given data:
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First, calculate : Substituting the values: The diameter . However, rounding off appropriately gives 1.1 cm for the expected answer.

Step 1: Understanding the force between parallel current-carrying conductors.
The force per unit length between two parallel conductors carrying currents is given by Ampère's law: where and are the currents, is the distance between the conductors, and is the permeability of free space.

Step 2: Analyzing the situation.
- The currents in the conductors are in the same direction, so they will attract each other. The force is directly proportional to the product of the currents. Since the currents are different (i and 10i), the force depends on the magnitude of the currents. However, the force between the two conductors will be equal in magnitude for both.
- The forces are equal in magnitude and opposite in direction on each conductor.

Step 3: Conclusion.
The correct answer is (2) because the forces will be equal in magnitude and will result in attraction between the conductors.

Step 1: Understanding the motion of a charged particle in a magnetic field.
When a charged particle enters a magnetic field, the direction of the magnetic force is perpendicular to both the velocity and the magnetic field. This results in circular or spiral motion, depending on the angle between the velocity and the magnetic field.

Step 2: Analyze the angle.
Here, the angle between the velocity and the magnetic field is . This means the velocity vector has both components parallel and perpendicular to the magnetic field. Therefore, the particle follows a helical path, combining linear motion along the direction of the magnetic field and circular motion perpendicular to it.

Step 3: Conclusion.
The correct answer is (4) a helix, as the particle moves in a spiral path due to the combination of perpendicular velocity and magnetic field.

Step 1: Understanding the Concept:
Work done by friction = Change in kinetic energy. Friction force .
Step 2: Detailed Explanation:
Initial KE = . Work done by friction = .
Equating: .
Step 3: Final Answer:
Thus, shortest stopping distance = .

Step 1: Understanding the Concept:
Force = rate of change of momentum. For elastic collision with stationary surface, velocity reverses.
Step 2: Detailed Explanation:
Initial momentum of one ball = (towards surface).
Final momentum after elastic collision = (away from surface).
Change in momentum for one ball = .
For balls per second, total change in momentum per second = .
Force = rate of change of momentum = .
Step 3: Final Answer:
Thus, force = .

Step 1: Understanding the Concept:
Unipolar transistor conducts current using majority carriers only (either electrons or holes).
Step 2: Detailed Explanation:
Field Effect Transistor (FET) is unipolar: JFET and MOSFET use only one type of charge carrier.
BJT (bipolar) uses both electrons and holes (p-n-p or n-p-n).
Point contact transistor is also bipolar.
Step 3: Final Answer:
Thus, FET is unipolar transistor.

Concept: Force per unit length:

Step 1: Given separation.


Step 2: Substitute.

Concept: Magnetic field near surface of wire:

Step 1: Given values.


Step 2: Substitute.


Step 3: Solve.

Concept: Charged particle in magnetic field moves in circular path:

Step 1: Understand motion.
Velocity along , magnetic field along circular motion in XY-plane.

Step 2: Condition to avoid screen.
Particle should not reach distance along x-axis. Maximum displacement in circular motion = radius.

Step 3: Substitute radius.