Magnetic Force

Step 1: Using the Formula for Peak Current The peak current in a capacitive circuit is given by: where:
- (capacitance),
- (angular frequency from the given equation),
- (peak voltage).

Step 2: Substituting Values Thus, the correct answer is .

Step 1: Using Einstein’s Photoelectric Equation The photoelectric equation is given by: where:
- is the incident photon energy,
- is the work function,
- is the maximum kinetic energy of the emitted electrons. Photon energy is related to wavelength by: where:
- eV·Å,
- is the wavelength in Å.

Step 2: Calculating Photon Energies For Å: For Å:

Step 3: Using the Given Condition Let the initial kinetic energy be , and the final kinetic energy be . Using the photoelectric equation: Substituting values: Solving for : Substituting in : Thus, the correct answer is .

Step 1: Understanding the motion of the electron
- The electron is initially moving downward due to gravity. - It enters a uniform magnetic field directed towards the south. - The force on a charged particle moving in a magnetic field is given by the Lorentz force: where: - is the charge of the electron ( ), - is the velocity vector of the electron, - is the magnetic field vector.

Step 2: Apply the Right-Hand Rule (Fleming's Left-Hand Rule)
- The velocity of the electron is downward ( ). - The magnetic field is directed towards the south ( ). - Using the cross-product : Since the electron has a negative charge, the force acts in the opposite direction to the computed cross-product, meaning the electron is deflected towards the east.

Step 1: Understanding the torque on a magnet in a magnetic field
The torque ( ) experienced by a magnet in a uniform magnetic field is given by: where: - is the magnetic moment of the magnet, - is the magnetic field strength, - is the angle between the magnetic moment and the field.

Step 2: Calculate the torque ratio
Initially, the angle is , so the initial torque is: Since , we get: When the angle is changed to , the new torque is: Since , we get:

Step 3: Find the percentage increase
The percentage increase in torque is given by: Substituting the values: Thus, the torque increases by 41.4\% when the angle changes from to .

Step 1: Understanding the Formula for Self-Inductance The self-inductance of a solenoid is given by: where:
- is the relative permeability of the core material,
- is the permeability of free space,
- is the number of turns,
- is the cross-sectional area,
- is the length of the solenoid.

Step 2: Effect of Changing the Core Material If the solenoid is initially empty (air core), the self-inductance is: When a diamagnetic material with relative permeability is inserted, the new inductance becomes: This shows that the self-inductance is reduced to half of its original value. Thus, the correct answer is becomes half.