A 2cmbl by 1.5cm rectangular coilhas 300 turns and rotates in a magnetic field B at 60Hz. What must the values of B be sobthat the maximum emf generated is 24v
To find the value of B, we can use the formula for the maximum emf generated in a rotating coil:
E_max = 2πfNAB,
where E_max is the maximum emf, f is the frequency (in Hz), N is the number of turns, A is the area of the coil, and B is the magnetic field.
Given:
E_max = 24 V
f = 60 Hz
N = 300
A = 2 cm * 1.5 cm = 3 cm^2 = 3 * 10^(-4) m^2
Plugging these values into the formula, we have:
24 V = 2π * 60 Hz * 300 * B * 3 * 10^(-4) m^2
Simplifying the equation:
24 V = 2π * 60 Hz * 300 * B * 3 * 10^(-4) m^2
24 V = 360π * B * 3 * 10^(-4) m^2
24 V = 1080π * B * 10^(-4) m^2
24 V = 108π * B * 10^(-4) m^2
Multiplying both sides by 10^4 to get rid of the exponent:
24 V * 10^4 = 108π * B * 10^(-4) m^2 * 10^4
240000 V = 108π * B m^2
Dividing both sides by 108π:
240000 V / (108π) = B m^2
B ≈ 708.4 T (approximately)
Therefore, the value of B must be approximately 708.4 T in order to generate a maximum emf of 24 V.