Electromagnetism - SS2 Physics Past Questions and Answers - page 4

Explanation: The time constant represents the time taken for the voltage across the capacitor to increase or decrease by approximately 63.2% (1 - 1/e) of its initial or final value.

Explanation: The time constant (τ) of an RC circuit is inversely proportional to the product of resistance (R) and capacitance (C). If C is doubled while R remains constant, τ = RC is doubled as well.

The time constant (τ) of an RC circuit is given by the product of resistance (R) and capacitance (C). τ = RC = (10,000 Ω) × (100 × 10^(-6) F) = 1 s.

The time constant (τ) of an RC circuit is given by the product of resistance (R) and capacitance (C). τ = RC = (220 Ω) × (47 × 10(-6) F) = 10.34 ms.

After one-time constant (τ), the voltage across the capacitor will reach approximately 63.2% of its final value. Therefore, the voltage across the capacitor after one time constant is 0.632 × 100 V = 63.2 V.

After two time constants (2τ), the voltage across the capacitor will reach approximately 86.5% of its final value. Therefore, the voltage across the capacitor after 6 ms is 0.865 × 200 V = 173 V.

A magnetic field is a region in space where magnetic forces are exerted on charged particles. It is created by moving charges or current-carrying conductors. When a charged particle moves through a magnetic field, it experiences a magnetic force perpendicular to both its velocity vector and the magnetic field direction. This force follows the right-hand rule, where the thumb points in the direction of the particle's velocity, the fingers point in the direction of the magnetic field, and the palm represents the direction of the magnetic force. This force can cause the particle to change its direction or move in a circular path, depending on the relative directions of the velocity and magnetic field.

For example, consider a positive charge moving to the right in a uniform magnetic field directed into the page. The magnetic force acting on the charge is directed downwards due to the right-hand rule. As a result, the charge experiences a centripetal force towards the centre of its circular path, causing it to move in a circle.

The motion of charged particles in magnetic fields depends on various factors, including the velocity of the particle, the magnetic field strength, and the angle between the velocity and magnetic field direction.

When a charged particle moves parallel or antiparallel to the magnetic field, it experiences no magnetic force. However, when the particle's velocity has a component perpendicular to the magnetic field, it experiences a magnetic force that causes it to move in a circular path. The radius of this path depends on the particle's velocity, the magnetic field strength, and the mass-to-charge ratio of the particle.

The trajectory of a charged particle can be affected by the angle between its velocity and the magnetic field. When the velocity is at an angle to the magnetic field, the particle moves along a helical path, combining the circular motion and the original direction of motion. The pitch of the helix depends on the angle and the ratio of the particle's charge to its mass.

Additionally, the motion of charged particles in magnetic fields can be used to determine their charge-to-mass ratio in devices like mass spectrometers or to deflect charged particles in particle accelerators.