A rotating search coil has 10 turns with a cross-sectional area of 5cm2. It rotates at constant speed of 100rpm. The output voltage is 80mV. Calculate magnetic field strength
To calculate the magnetic field strength, also known as magnetic flux density, we can use Faraday's law of electromagnetic induction. This law states that the induced electromotive force (EMF) or voltage in a coil is directly proportional to the rate of change of the magnetic flux passing through the coil.
The formula to calculate the induced voltage is:
EMF = -NΔ(BA) / Δt
Where:
EMF is the induced electromotive force or voltage (in volts)
N is the number of turns of the coil
Δ(BA) is the change in magnetic flux, which is the product of the magnetic field strength (B) and the cross-sectional area (A) of the coil (in Weber, Wb)
Δt is the time interval in which the change occurs (in seconds)
In this case, we have the following values:
N = 10 turns
A = 5 cm² = 5 × 10⁻⁴ m² (since 1 cm² = 10⁻⁴ m²)
EMF = 80 mV = 80 × 10⁻³ V (since 1 V = 10³ mV)
Δt = 1 minute = 60 seconds (since 1 minute = 60 seconds)
Rearranging the equation to solve for magnetic field strength (B), we get:
B = -EMF x Δt / (N x A)
Substituting the given values:
B = -(80 × 10⁻³ V) x (60 s) / (10 turns x 5 × 10⁻⁴ m²)
B = -(80 × 10⁻³ V) x (60 s) / (10 turns x 5 × 10⁻⁴ m²)
B = -0.048 T
The negative sign indicates that the direction of the magnetic field is opposite to the direction of the current flow in the coil.
Therefore, the magnetic field strength is approximately 0.048 Tesla.