Question

Suppose a 6.00 nC electric charge is in the beam. What is the maximum electric force (in N) it experiences? If the static charge moves at 300 m/s, what maximum magnetic force (in N) can it feel?

Answer 1

Complete Question

Electromagnetic radiation from a 3.00 mW laser is concentrated on a 2.00 mm2 area. Suppose a 6.00 nC electric charge is in the beam. What is the maximum electric force (in N) it experiences? If the static charge moves at 300 m/s, what maximum magnetic force (in N) can it feel?

Answer:

The value are

`F = 6.378 *10^(-6) \ N`

and

`F_k = 6.381 *10^(-12) \ N`

Step-by-step explanation:

From the question we are told that

The power of the laser is
`P = 3.00 mW = 3.00*10^(-3) \ W`

The area is
`A = 2.00 \ mm^2 = 2.0 *10^(-6) \ m^2`]

The speed is
`v = 300 \ m/s`

The magnitude of the electric charge is
`Q = 6.00 nC = 6.00 *10^(-9) \ C`

Generally the intensity of the beam is mathematically represented as

`I = (P)/(A)`

=>
`I = (3.00 *10^(-3))/( 2.0 *10^(-6))`

=>
`I = 1500 \ W/m^2`

Generally the magnitude of the electric field is mathematically represented as

`E_m = \sqrt{(2I)/(c \epsilon_o) }`

Here c is the speed of light with value
`c = 3.0*10^(8) \ m/s`

`\epsilon_o` is the permittivity of free space with value
`\epsilon_o = 8.85*10^(-12) C/(V \cdot m)`

`E_m = \sqrt{(2 * 1500 )/(3.0*10^(8) *8.85*10^(-12) ) }`

=>
`E_m = 1063 \ V/m`

Generally the maximum electric force is mathematically represented as

`F = Q * E_m`

=>
`F = 6*10^(-9 ) * 1063`

=>
`F = 6.378 *10^(-6) \ N`

Generally the intensity of the beam can also be mathematically represented as

`I = ( c * B^2 )/( 2 * \mu_o)`

Here B is the magnetic field

`\mu_o` is the permeability of free space with value
`\mu_o = 4\pi * 10^(-7) N/A^2`

So

`B = \sqrt{(2 * \mu_o * I )/(c) }`

=>
`B = \sqrt{(2 * 4 \pi *10^(-7) * 1500 )/(3.0*10^(8)) }`

=>
`B = 3.545*10^(-6) \ T`

Generally the maximum magnetic force is mathematically represented as

`F_k = Q * v * B`

=>
`F_k = 6.00 *10^(-9) * 300 * 3.545*10^(-6)`

=>
`F_k = 6.381 *10^(-12) \ N`