A beam of light travelling along x-axis is described by the magnetic field, `E_y=(600 Vm^-1) sin omega (t-x//c)`
Calculating the maximum electric and magnetic forces on a charge q=2e,
moving along y-axis with a speed of `3xx10^7m//s`, where `e=1.6xx10^(-19)C`.

Explanation

To solve the problem, we need to calculate the maximum electric and magnetic forces on a charge \( q = 2e \) moving along the y-axis with a speed of \( 3 \times 10^7 \, \text{m/s} \). Here, \( e = 1.6 \times 10^{-19} \, \text{C} \).

### Step 1: Calculate the Maximum Electric Force

The electric field is given by:

\[ E_y = 600 \, \text{V/m} \cdot \sin(\omega(t - \frac{x}{c})) \]

The maximum electric field \( E_{\text{max}} \) is \( 600 \, \text{V/m} \). The electric force \( F_E \) on a charge \( q \) is given by:

\[ F_E = qE \]

Substituting \( q = 2e = 2 \times 1.6 \times 10^{-19} \, \text{C} \):

\[ F_E = (2 \times 1.6 \times 10^{-19}) \times 600 \]

Calculating this:

\[ F_E = 3.2 \times 10^{-19} \times 600 = 1.92 \times 10^{-16} \, \text{N} \]

### Step 2: Calculate the Magnetic Field

The magnetic field \( B \) can be calculated using the relationship between the electric field \( E \) and the speed of light \( c \):

\[ B = \frac{E}{c} \]

Where \( c = 3 \times 10^8 \, \text{m/s} \). Thus,

\[ B = \frac{600}{3 \times 10^8} = 2 \times 10^{-6} \, \text{T} \]

### Step 3: Calculate the Magnetic Force

The magnetic force \( F_B \) on a charge moving with velocity \( v \) in a magnetic field \( B \) is given by:

\[ F_B = qvB \sin(\theta) \]

Since the charge is moving along the y-axis and the magnetic field is perpendicular to this direction, \( \theta = 90^\circ \) and \( \sin(90^\circ) = 1 \):

\[ F_B = qvB \]

Substituting the values:

\[ F_B = (2 \times 1.6 \times 10^{-19}) \times (3 \times 10^7) \times (2 \times 10^{-6}) \]

Calculating this:

\[ F_B = (3.2 \times 10^{-19}) \times (3 \times 10^7) \times (2 \times 10^{-6}) \]

\[ F_B = 3.2 \times 3 \times 2 \times 10^{-19} \times 10^1 = 19.2 \times 10^{-18} = 1.92 \times 10^{-17} \, \text{N} \]

### Summary of Results

- Maximum Electric Force \( F_E = 1.92 \times 10^{-16} \, \text{N} \)
- Maximum Magnetic Force \( F_B = 1.92 \times 10^{-17} \, \text{N} \)

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