Two observers moving with different velocities observes a moving charge. Then at a point $A$ whose position vector from the point charge is $\vec{r}$ , mark the correct statement(s).

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

If magnetic field measured by two observers is same then their relative velocity must be parallel or antiparallel to $\vec{r}$ .

The magnitude of magnetic field measured by two observers may be same.

The magnitude of magnetic field measured by two observers must be same.

The magnetic field measured by two observers may be different.

answer is A, C, D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The magnetic field due to a moving charge at any point is given by $\vec{B} = \frac{μ_{0} q (\vec{v} \times \vec{r})}{4 {πr}^{3}}$ where $\vec{v}$ is the velocity of charge with respect to observer.

Let $\vec{v_{1}} & \vec{v_{2}}$ be the velocities of two observers with respect to ground then

${\vec{B}}_{1} = \frac{μ_{0} q [(\vec{v} - {\vec{v}}_{1}) \times \vec{r}}{4 {πr}^{3}} & {\vec{B}}_{2} = \frac{μ_{0} q [(\vec{v} - {\vec{v}}_{2}) \times \vec{r}}{4 {πr}^{3}}$

Where $\vec{v}$ is the velocity of charge with respect to ground ${\vec{B}}_{1} = {\vec{B}}_{2} w h e n (\vec{v} - {\vec{v}}_{1}) \times \vec{r} = (\vec{v} - {\vec{v}}_{2}) \times \vec{r} \Rightarrow ({\vec{v}}_{2} - {\vec{v}}_{1}) \times \vec{r} = 0 \Rightarrow ({\vec{v}}_{21}) \times \vec{r} = 0 \Rightarrow {\vec{v}}_{21} ∥ \vec{r}$