Question

Let →E and →B denote electric and magnetic fields in a frame S and →E' and →B' in another frame S' moving with respect to S at a velocity →v . Two of the following equations are wrong. Identify them.
(a) By'=By+vEzc2
(b) Ey'=Ey-vBzc2
(c) By' = By + vEz
(d) Ey' = Ey + vBz

Answer 1

Two of the incorrect equations are:

(b) Ey'=Ey-vBzc2,

(c) By’ = By+vEz.

Explanation:

• The magnetic force of a charged particle is q V B and the electric force is q E.

• Using dimensional analysis, two wrong equations can be sorted out. Now, when the above two forces are equated, we obtain:

                                  $E=V B$

• So, using dimensional analysis, examining the answers, we observe that on the RHS of the equations (b) and (c), the second term are not correct dimensionally. Thus, the options (c) and (b) are incorrect.