Q.

A student determines a dimensionless quantity, B=en2ε0hc. Find the value of n. (Here, e = electric charge, ε0 = electric permittivity of vacuum, h = Planck's constant and c = speed of light.)

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answer is 2.

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Detailed Solution

Dimension of B=M0L0T0Dimension e=[AT]Dimension ε0=A2M−1L−3T4Dimension h=ML2T−1Dimension c=LT−1∴M0L0T0=[AT]nA2M−1L−3T4ML2T−1LT−1 or M0L0T0=An−2L0Tn−2∴n−2=0⇒n=2
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A student determines a dimensionless quantity, B=en2ε0hc. Find the value of n. (Here, e = electric charge, ε0 = electric permittivity of vacuum, h = Planck's constant and c = speed of light.)