Electromagnetism

Step 1: Understanding the Motion of the Charged Particle
A charged particle moving in a magnetic field experiences a force given by: Where:
is the charge of the particle,
is the velocity of the particle,
is the magnetic field.
The force due to the magnetic field is always perpendicular to the velocity of the particle.
Step 2: Analyzing the Components of Velocity
When the velocity has a component parallel to the magnetic field , the particle will experience no force along that direction, and will continue to move in the same direction.
When there is a component of velocity perpendicular to the magnetic field, the particle will experience a force and undergo circular motion in a plane perpendicular to the magnetic field.
The combination of these two components of velocity (along and perpendicular to the magnetic field) results in a helical motion. The particle moves in a spiral path around the magnetic field lines.
Step 3: Conclusion
The path of the charge particle will be a helical path with the axis along the direction of the magnetic field. This is because the component of velocity along causes the particle to move parallel to the field, while the perpendicular component causes circular motion around the field lines.

Final Answer: The path of the charge particle will be a helical path with the axis along magnetic field .

Step 1: Understanding the Problem
A cylinder contains helium gas at standard temperature and pressure (STP). The volume of the cylinder is 44.8 litres. We need to calculate the amount of heat required to raise the temperature of the gas by 20.0°C.
Step 2: Calculating the Number of Moles of Helium
At STP, 1 mole of an ideal gas occupies 22.4 litres. Therefore, the number of moles ( ) of helium in 44.8 litres is:
Step 3: Using the Heat Capacity at Constant Volume
For a monatomic gas like helium, the molar heat capacity at constant volume ( ) is:
Given :
Step 4: Calculating the Heat Required
The heat ( ) required to raise the temperature by is:
Substituting the values:
Step 5: Matching with the Options
The calculated heat required is 498 J, which corresponds to option (C). Final Answer: The amount of heat needed is 498 J.