Question

Two large parallel plates move with a constant speed v in the positive y-direction as shown in the figure. If both the plates have a surface charge density $\sigma >0$, the magnetic field at the point P just above the top plate will have

• A. larger magnitude than the field at the mid-point between the plates and point towards -$\hat{x}$.
• B. smaller magnitude than the field at the mid-point between the plates and point towards -$\hat{x}$.
• C. larger magnitude than the field at the mid-point between the plates and point towards +$\hat{x}$.
• D. smaller magnitude than the field at the mid-point between the plates and point towards +$\hat{x}$.

Answer 1

The correct option is C larger magnitude than the field at the mid-point between the plates and point towards +$\hat{x}$.

As we can see from figure plates are moving in $+vey$ direction therefore, direction of current will be in positive y direction .
Now applying $\overrightarrow{dl}\times \overrightarrow{r}$ we find that direction of field just above point P is in $+vexdirection$.
Now just above point P field has some magnitude but at the center of plates magnetic field due to each plate cancel each other because they both are in opposite direction.
At mid point field due to upper plate is in $-vex$ direction and field due to lower plate is in $+ve$ x direction and both are equal in magnitude therefore, at mid point field is zero.