In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, E andB stand for dimensions of electric and magnetic fields respectively, while ε$$0$$ andμ$$0$$ stand for dimensions of the permittivity and permeability of free space respectively. L andT are dimensions of length and time respectively. All the quantities are given in SI units. The relation between E andB isThe relation between ε$$0$$ and μ$$0$$ is

Question

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, E andB stand for dimensions of electric and magnetic fields  respectively, while ε$$0$$ andμ$$0$$ stand for dimensions of the permittivity and permeability of free space respectively. L andT are dimensions of length and time respectively. All the quantities are given in SI units. The relation between E andB  isThe relation between  ε$$0$$  and μ$$0$$ is

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We have  $$EC=B$$⇒EL−$$1T1=B$$⇒$$E=BLT-1We$$ have ∴$$C2=1$$μ$$0$$ε$$0$$⇒$$L2T$$−$$2=1$$μ$$0$$ε$$0$$⇒μ$$0=$$ε$$0$$−$$1L$$−$$2T2$$

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