A stationary particle of charge q = 1.4 10-8 C is placed in a laser beam (an electromagnetic wave) whose intensity is 3.5 103 W/m2. Determine the magnitudes of the (a) electric and (b) magnetic forces exerted on the charge. If the charge is moving at a speed of 3.7 104 m/s perpendicular to the magnetic field of the electromagnetic wave, find the magnitudes of the (c) electric and (d) magnetic forces exerted on the particle.
(a)
(b)
(c)
(d)
Don't you have standard force equations for moving particles in magnetic fields, and charges in E fields to do this?
To determine the magnitudes of the electric and magnetic forces exerted on the charge, we can use the formulas that relate these forces to the charge and the properties of the electromagnetic wave.
(a) Electric Force:
The electric force exerted on a charged particle is given by the equation:
F_electric = q * E
where q is the charge of the particle and E is the electric field intensity of the electromagnetic wave.
To find the electric force, we need to calculate the electric field intensity, which can be obtained using the formula:
E = sqrt(intensity / (2 * epsilon_0 * c))
where intensity is the intensity of the laser beam, epsilon_0 is the vacuum permittivity (8.85 x 10^-12 C^2/N*m^2), and c is the speed of light (3 x 10^8 m/s).
Substituting the given values, we can calculate E:
E = sqrt(3.5 x 10^3 W/m^2 / (2 * 8.85 x 10^-12 C^2/N*m^2 * 3 x 10^8 m/s))
(b) Magnetic Force:
The magnetic force exerted on a charged particle moving perpendicular to the magnetic field of an electromagnetic wave is given by the equation:
F_magnetic = q * v * B
where q is the charge of the particle, v is its velocity, and B is the magnetic field intensity of the electromagnetic wave.
To find the magnetic force, we need to calculate the magnetic field intensity, which can be obtained using the formula:
B = sqrt(intensity / (2 * epsilon_0 * c))
where intensity is the intensity of the laser beam, epsilon_0 is the vacuum permittivity (8.85 x 10^-12 C^2/N*m^2), and c is the speed of light (3 x 10^8 m/s).
Substituting the given values, we can calculate B:
B = sqrt(3.5 x 10^3 W/m^2 / (2 * 8.85 x 10^-12 C^2/N*m^2 * 3 x 10^8 m/s))
(c) Electric Force with Motion:
To calculate the electric force on a moving charge, we need to consider the Lorentz force. The electric force becomes:
F_electric = q * E + q * v * B
where q is the charge of the particle, E is the electric field intensity of the electromagnetic wave, v is the velocity of the particle, and B is the magnetic field intensity of the electromagnetic wave.
Substituting the given values, we can calculate F_electric.
(d) Magnetic Force with Motion:
The magnetic force on a moving charge can be calculated using the formula:
F_magnetic = q * v * B
where q is the charge of the particle, v is its velocity, and B is the magnetic field intensity of the electromagnetic wave.
Substituting the given values, we can calculate F_magnetic.