How is a sine wave created?

How is a sine wave created?

• A. A straight wire with constant current
• B. A capacitor charging with DC
• C. A wire loop rotating within a magnetic field
• D. A coil connected to a battery

Answer: (C)

A sine wave is produced when the emf in a circuit varies sinusoidally over time, which happens most cleanly when magnetic flux through a coil changes in a smooth, repeating way. If a coil or loop rotates in a steady magnetic field, the magnetic flux through the loop changes as the cosine of the rotation angle. With constant angular speed, the flux is Φ = B A cos(ωt). The induced emf is the negative time derivative of the flux: E = -N dΦ/dt = N B A ω sin(ωt). That sine-shaped voltage (and the resulting current in a closed circuit) is the sine wave. The other scenarios don’t produce a continuous sine wave. A straight wire with constant current creates a steady magnetic field but no changing flux to generate an alternating voltage. Capacitor charging with DC produces a transient current that dies out to zero, not a repeating wave. A coil connected to a battery provides direct current, not alternating current.

A sine wave is produced when the emf in a circuit varies sinusoidally over time, which happens most cleanly when magnetic flux through a coil changes in a smooth, repeating way. If a coil or loop rotates in a steady magnetic field, the magnetic flux through the loop changes as the cosine of the rotation angle. With constant angular speed, the flux is Φ = B A cos(ωt). The induced emf is the negative time derivative of the flux: E = -N dΦ/dt = N B A ω sin(ωt). That sine-shaped voltage (and the resulting current in a closed circuit) is the sine wave.

The other scenarios don’t produce a continuous sine wave. A straight wire with constant current creates a steady magnetic field but no changing flux to generate an alternating voltage. Capacitor charging with DC produces a transient current that dies out to zero, not a repeating wave. A coil connected to a battery provides direct current, not alternating current.