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  • Two observers moving with different velocities see that a point charge produces same magnetic field at the same point A . Their relative velocity must be parallel to , where  is the position v

Two observers moving with different velocities see that a point charge produces same magnetic field at the same point A . Their relative velocity must be parallel to , where  is the position vector of point A with respect to point charge. This statement is :

Option: 1

true


Option: 2

false


Option: 3

nothing can be said


Option: 4

true only if the charge is moving prependicular to the


Answers (1)

 

In Vector Form -

- wherein

 

 

Since,

\overrightarrow{B} = \frac{\mu_{0}}{4\pi}q\frac{\overrightarrow{v}\times \overrightarrow{r}}{r^{3}}, \overrightarrow{v}\times \overrightarrow{r} must be same

where  \overrightarrow{v} = velocity of charge with respect to observer

 Let then A and B are the observers

then \left ( \overrightarrow{v} _{c}- \overrightarrow{v}_{A}\right )\times \overrightarrow{r} = \left ( \overrightarrow{v}_{C}- \overrightarrow{v}_{B} \right )\times \overrightarrow{r}

\left ( \overrightarrow{v} _{A}- \overrightarrow{v}_{B}\right )\times \overrightarrow{r} = 0 or \left ( \overrightarrow{v}_{A}- \overrightarrow{v}_{B} \right )\left | \right | \overrightarrow{r}

Posted by

Sumit Saini

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