Physics, 08.12.2020 16:40 barclaybarnes07

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?

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Answer from: kah36

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?

The value are

$F = 6.378 *10^{-6} \ N$

and

$F_k = 6.381 *10^{-12} \ N$

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

$I = \frac{P}{A}$

=> $I = \frac{3.00 *10^{-3}}{ 2.0 *10^{-6}}$

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

Generally the magnitude of the electric field is mathematically represented as

$E_m = \sqrt{\frac{2I}{c \epsilon_o} }$

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 $\epsilon_o = 8.85*10^{-12} C/(V \cdot m)$

$E_m = \sqrt{\frac{2 * 1500 }{3.0*10^{8} *8.85*10^{-12} } }$

=> $E_m = 1063 \ V/m$

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

$I = \frac{ c * B^2 }{ 2 * \mu_o}$

Here B is the magnetic field

$\mu_o$ is the permeability of free space with value $\mu_o = 4\pi * 10^{-7} N/A^2$

$B = \sqrt{\frac{2 * \mu_o * I }{c} }$

=> $B = \sqrt{\frac{2 * 4 \pi *10^{-7} * 1500 }{3.0*10^{8}} }$

=> $B = 3.545*10^{-6} \ T$

Generally the maximum magnetic force is mathematically represented as

F_k = Q * v * B

=> $F_k = 6.00 *10^{-9} * 300 * 3.545*10^{-6}$

=> $F_k = 6.381 *10^{-12} \ N$

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Answer from: Quest

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Suppose a 6.00 nC electric charge is in the beam. What is the maximum electric force (in N) it exper...

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