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-

The correct options are A E_y'=E_y vB_z/c^2 C B_y'=B_y+vE_z From Lorentz transformation, E_y^'= γ (E_y vB_z) B_y^'= γ (B_y +v/c^2E_z) where ...

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Byju's Answer

Standard XII

Physics

Instantaneous Velocity

Let E⃗ and ...

Question

Let $\to E$ and $\to B$ denote electric and magnetic fields in a frame S and ${\to E}^{'}$ and ${\to B}^{'}$ in another frame S' moving with respect to S at a velocity $\to v$ . Two of the following equations are wrong. Identify them:

B_{y}^{'} = B_{y} + \frac{v E_{z}}{c^{2}}

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E_{y}^{'} = E_{y} - \frac{v B_{z}}{c^{2}}

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B_{y}^{'} = B_{y} + v E_{z}

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E_{y}^{'} = E_{y} - v B_{z}

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Solution

The correct options are
A $E_{y}^{'} = E_{y} - \frac{v B_{z}}{c^{2}}$
C $B_{y}^{'} = B_{y} + v E_{z}$
From Lorentz transformation,
$E_{y}^{^{'}} = γ (E_{y} - v B_{z})$
$B_{y}^{^{'}} = γ (B_{y} + \frac{v}{c^{2}} E_{z})$
where $γ = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$ where the symbols have their usual meaning.
when $\frac{v}{c} << 1$ $γ = 1$ , then the the transformation equations will hold.

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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:

The correct options are A E′y=Ey−vBzc2 C B′y=By+vEzFrom Lorentz transformation,E′y=γ(Ey−vBz)B′y=γ(By+vc2Ez)where γ=1√1−v2c2 where the symbols have their usual meaning.when vc<<1 γ=1, then the the transformation equations will hold.

Let $\to E$ and $\to B$ denote electric and magnetic fields in a frame S and ${\to E}^{'}$ and ${\to B}^{'}$ in another frame S' moving with respect to S at a velocity $\to v$ . Two of the following equations are wrong. Identify them: