Physics

In the formula $$X=3YZ^2$$, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are ________.


ANSWER

$$-3$$ in mass, $$-2$$ in length, $$4$$ in time and $$4$$ in charge.


SOLUTION
Given,

$$X=3YZ^2$$

Then,

$$Y=\dfrac{X}{3Z^2}$$

$$[X]=[C]=[M^{-1}L^{-2}T^2Q^2]$$

$$[Z]=[B]=[MT^{-1}Q^{-1}]$$

Then,

$$[Y]=\dfrac{[X]}{[3Z^2]}$$

$$=\dfrac{[M^{-1}L^{-2}T^2Q^2]}{[MT^{-1}Q^{-1}]^2}=[M^{-3}L^{-2}T^4Q^4]$$

That is,

$$-3$$ in mass, $$-2$$ in length, $$4$$ in time and $$4$$ in charge.
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