Concepts Of Physics MCQ Edition [Volume 2]PhysicsMagnetic Field
Suppose E and B represent the electric and magnetic fields in a reference frame S , while E ' and B ' represent them in another frame S' that moves with a velocity v relative to S . Which two of the following equations are incorrect?
Options
- AE_y' = E_y - v B_z
- BE_y' = E_y - v B_z c^2
- CB_y' = B_y + v E_z
- DB_y' = B_y + v E_z c^2
Correct answer
C. B_y' = B_y + v E_z
Step-by-step solution
The Lorentz transformations for the transverse components of electric and magnetic fields in SI units, for a frame S' moving with velocity v along the x-axis relative to S , are given by: E_y' = (E_y - v B_z) B_y' = (B_y + v c^2 E_z ) where = 1 1 - v^2/c^2 . For non-relativistic speeds ( v c ), 1 , and the equations approximate to: E_y' E_y - v B_z B_y' B_y + v c^2 E_z This can also be verified using dimensional analysis. In SI units, the dimensions of electric field E and magnetic field B are related by [E] = [vB]