Question

An electromagnetic wave travelling in \(x\)-direction is described by the field equation} \[ E_y = 300 \sin \omega\left(t - \frac{x}{c}\right). \] If the electron is restricted to move in \(y\)-direction only with speed \(1.5 \times 10^6\) m/s, then the ratio of maximum electric and magnetic forces acting on the electron is:

• A. \(200\)
• B. \(150\)
• C. \(400\)
• D. \(300\)

Answer 1

The Correct Option is A

Concept: Electric force on electron: \[ F_E = eE \] Magnetic force: \[ F_B = evB \] For electromagnetic waves: \[ B = \frac{E}{c} \]
Step 1:Write the force ratio} \[ \frac{F_E}{F_B} = \frac{eE}{evB} \] \[ = \frac{E}{vB} \]
Step 2:Substitute \(B = E/c\)} \[ \frac{F_E}{F_B} = \frac{E}{v(E/c)} \] \[ = \frac{c}{v} \]
Step 3:Substitute values} \[ c = 3\times10^8 \text{ m/s} \] \[ v = 1.5\times10^6 \text{ m/s} \] \[ \frac{F_E}{F_B} = \frac{3\times10^8}{1.5\times10^6} \] \[ = 200 \] Thus \[ \boxed{200} \]