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. 1. B_y,=B_y+ vE_z c^2 2. E_y,=E_y+ vB_z c^2 3. B'_y=B_y+vE_z 4. E'_y=E_y+vB_z

2. E_y,=E_y+ vB_z c^2 3. B'_y=B_y+vE_z Explanation: qE=qvB =vB By dimensionally b & care wrong =v^2B = vE v ^2

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

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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