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Question
The dimensions of the rate of change of magnetic flux are ______.
Options
[M L T−3 A]
[M L2 T−3 A−1]
[M L2 T−2 A−1]
[M L2 T−3 A−2]
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Solution
The dimensions of the rate of change of magnetic flux are [M L2 T−3 A−1].
Explanation:
According to Faraday’s Law of Electromagnetic Induction, the induced EMF (ε) is equal to the negative rate of change of magnetic flux (dΦ/dt).
Therefore, the dimensions of the rate of change of magnetic flux are identical to the dimensions of EMF (Potential difference).
EMF (V) is defined as work done per unit charge:
V = `W/q`
Dimensions of Work (W) = [M L2 T−2]
Dimensions of Charge (q) = [A T]
Substitute the dimensions into the formula for V:
[V] = `([M L^2 T^-2])/([A T])`
= [M L2 T−3 A−1]
Since `(d phi)/dt` = ε, the dimensions of the rate of change of magnetic flux are [M L2 T−3 A−1].
