Let E and B denote electric and magnetic fields in a frame S and … - Vidyadip

Question

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

$\text{B}_\text{y},=\text{B}_\text{y}+\frac{\text{vE}_\text{z}}{\text{c}^2}$
$\text{E}_\text{y},=\text{E}_\text{y}+\frac{\text{vB}_\text{z}}{\text{c}^2}$
$\text{B}'_\text{y}=\text{B}_\text{y}+\text{v}\text{E}_\text{z}$
$\text{E}'_\text{y}=\text{E}_\text{y}+\text{vB}_\text{z}$

✓

Answer

$\text{E}_\text{y},=\text{E}_\text{y}+\frac{\text{vB}_\text{z}}{\text{c}^2}$
$\text{B}'_\text{y}=\text{B}_\text{y}+\text{v}\text{E}_\text{z}$

Explanation:
$\text{qE}=\text{qvB}$
$\Rightarrow\text{e}=\text{vB}$ By dimensionally b & care wrong
$\Rightarrow\text{v}\text{E}=\text{v}^2\text{B}$
$\Rightarrow\text{B}=\frac{\text{vE}}{\text{v} ^2}$

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