Q. The magnetic field in the plane electromagnetic field is given by $B_{y} = 2 \times 10^{- 7}\sin{\left( 0.5 \times 10^{3}z + 1.5 \times 10^{11}t \right)T}$ The expression for the electric field may be given by
A) $E_{y} = 2 \times 10^{- 7}\sin{(0.5 \times 10^{3}z + 1.5 \times 10^{11}t)}V/m$
B) $E_{x} = 2 \times 10^{- 7}\sin{(0.5 \times 10^{3}z + 1.5 \times 10^{11}t)}V/m$
C) $E_{y} = 60\sin{\left( 0.5 \times 10^{3}z + 1.5 \times 10^{11}t \right)V/m}$
D) $E_{x} = 60\sin{\left( 0.5 \times 10^{3}z + 1.5 \times 10^{11}t \right)V/m}$
Explanation
(d) $B_{y} = 2 \times 10^{- 7}\sin{(0.5 \times 10^{3}z + 1.5 \times 10^{11}t)T}$
The electric vector is perpendicular to $B$ as well as direction of propagation of electromagnetic wave.
Therefore $E_{x}$ has to be taken.
Further, $E_{0} = B_{0} \times c \Rightarrow 2 \times 10^{- 7} \times 3 \times 10^{8}V/m = 60V/m$
$\therefore$ The corresponding value of the electric field is
$E_{x} = 60\sin{\left( 0.5 \times 10^{3}z + 1.5 \times 10^{11}t \right)V/m}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.