Question

The magnetic field of a plane electromagnetic wave is given by $\vec{B} = B_0 \hat{i} [cos (kz - \omega t)] + B_1 \hat{j} cps (kz + \omega t).$ where B$_0 = 3 � 10^{-5} T$ and B$_1 = 2 � 10^{-6}$ T. The rms value of the force experienced by a stationary charge Q = 10 C at z = 0 is closest to :

• A. $0.9 \,N$
• B. $0.1 \,N$
• C. $3 \times 10^-2\, N$
• D. $0.6\, N$

Answer 1

The Correct Option is D

Maximum Electric field E = (B) (c) $\vec{E_0} = (3 \times 10^{-5})c (-\hat{j})$ $\vec{E_1} = (3 \times 10^{-6})c (-\hat{i})$ Maximum force $\vec{F}_{net} = q\vec{E} = qc (-3 \times 10^{-5} \hat{j} - 2 \times 10^{-6} \hat{i})$ $\vec{F}_{0max} \, = \, 10^{-4} \times 3 \times 10^8 \sqrt{(3 \times 10^{-5})^2 + (2 \times 10^{-6})^2}$ $= 0.9 N$ $F_{rms} = \frac{F_0}{\sqrt{2}} \, = \, 0.6 N \, \, \, \, \, \, \, \, (approx)$ Option (4)