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If E is the electric field and B is the magnetic field, then the dimensions of E/B are ________.

Asked in GSEB Board March 2016 · Units and dimensions

Answer: (2) M⁰L¹T⁻¹

Step-by-step solution

Given: the electric field E and the magnetic field B.

Idea: get each from a force. E=F/q gives [E]=M¹L¹T⁻³A⁻¹, and F=BIℓ gives [B]=M¹L⁰T⁻²A⁻¹.

([E])/([B])=(M¹L¹T⁻³A⁻¹)/(M¹L⁰T⁻²A⁻¹)=M⁰L¹T⁻¹ -- mass and current both cancel.

What is left is the dimension of a speed, and that is no accident: balancing the electric and magnetic forces on a moving charge, qE=qvB, gives v=E/B, and in an electromagnetic wave (E₀)/(B₀)=c.

So E/B has the dimensions M⁰L¹T⁻¹.

Why the other options are wrong

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