Question

Verify that the units of ΔΦ/ Δt are volts. That is, show that:

(A) 1 T⋅m²/s = 1 V
(B) 1 V = 1 T⋅m²/s
(C) 1 T = 1 V/s⋅m²
(D) 1 V/s = 1 T⋅m²

Answer 1

The units of magnetic flux change per unit time, ΔΦ/Δt, are shown to be equivalent to volts by relating the Tesla unit to Newton per ampere-meter and using the definitions of the Joule and Coulomb, resulting in 1 T·m²/s equaling 1 V.

Step-by-step explanation:

To verify that the units of ΔΦ/Δt are volts, we look at the relationship between magnetic flux (Φ), time (t), the Tesla (T), meters squared (m²), and seconds (s). The magnetic flux change per unit time, ΔΦ/Δt, is measured in volts according to Faraday's law of electromagnetic induction. The unit Tesla (T) is one Newton per ampere-meter (N/(Am)). Thus, 1 T is equal to 1 N/A·m. A Volt (V) is defined as one Joule per Coulomb (J/C), and since a Joule is a Newton-meter (N·m) and a Coulomb is an Ampere-second (A·s), we can express 1 V as 1 (N·m)/(A·s). By substituting our Tesla unit, we can define 1 T·m²/s as 1 V, completing the verification as follows:

1 T·m²/s = (1 N/A·m) · m²/s = 1 N·m/s · (1/A) = 1 J/s · (1/C) = 1 V