Moving Charges And Magnetism

Step 1: Formula for magnetic flux.
The magnetic flux through a solenoid is given by: where: - is the magnetic field, - is the area of cross-section of the solenoid, - is the number of turns, - is the current.
Step 2: Substituting the known values.
The total flux will depend on the current and the length . The flux produced will be 60 Wb.
Step 3: Conclusion.
Thus, the magnetic flux is , so the correct answer is (B).

Step 1: Understanding the magnetic field behavior.
In the case of a solenoid or a magnetic field around a wire, the magnetic field strength decreases with distance from the source (such as the center of the solenoid or the current-carrying wire).
Step 2: Conclusion.
The magnetic field typically decreases as increases, so the correct answer is (B).

Step 1: Understanding magnetic dipoles.
A magnetic dipole consists of two equal and opposite magnetic charges separated by a small distance. The dipole moment is directed from the negative to the positive pole.
Step 2: Analyzing the field behavior.
When placed in an external magnetic field, the dipole tends to align with the field. The field lines form a dipole pattern around the magnetic charges.
Step 3: Conclusion.
Thus, the magnetic dipole forms a dipole in the external magnetic field. The correct answer is (C).

Step 1: Force formula in a magnetic field.
The force experienced by a current-carrying conductor in a magnetic field is given by the equation: where:
- (magnetic field strength),
- (current),
- (length of the conductor in the field).
Step 2: Calculating the force.
Substituting the values into the equation:
Step 3: Conclusion.
The correct answer is , so the correct answer is (A).

Step 1: Formula for magnetic dipole moment.
The magnetic dipole moment of a solenoid is given by: where: - is the number of turns per unit length, - is the current flowing through the solenoid, - is the area of the solenoid's cross section.
Step 2: Using the given values.
We are given the magnetic field strength , and for a long solenoid, we know that , where . By rearranging for and substituting into the formula for , we calculate the magnetic dipole moment.
Step 3: Conclusion.
The magnetic dipole moment is , so the correct answer is (D).

Step 1: Understanding the Concept:
When a charged particle moves perpendicularly to a magnetic field, the magnetic force ( ) provides the necessary centripetal force ( ).
Step 2: Formula Derivation:
Equating the forces: .
The time period is the circumference divided by speed: $ T v R$).

Step 1: Understanding the Concept:
The magnetic field due to a straight wire is . The direction is determined by the Right-Hand Thumb Rule.
Step 2: Detailed Explanation:
Magnitude: $ 1.2 \times 10^{-5} r I 1.2 \times 10^{-5}$ T (rounded) towards the South.

Step 1: Understanding the Concept:
Current Sensitivity ( ) is . Voltage Sensitivity ( ) is .
Step 2: Detailed Explanation:
1. Current Sensitivity: . If turns ( ) are doubled, is doubled.
2. Voltage Sensitivity: . When is doubled, the length of the wire doubles, which also doubles the resistance ( ).
Since both the numerator ( ) and denominator ( ) double, the ratio remains constant.
Step 3: Final Answer:
Current sensitivity doubles, but voltage sensitivity remains unchanged.