A magnetic field has a magnitude of 1.20 10-3 T, and an electric field has a magnitude of 5.50 103 N/C. Both fields point in the same direction. A positive 1.8-µC charge moves at a speed of 2.60 106 m/s in a direction that is perpendicular to both fields. Determine the magnitude of the net force that acts on the charge.
__________ N
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To determine the magnitude of the net force acting on the charge, we can use the equation for the force experienced by a moving charge in a magnetic field:
F = q * v * B * sinθ
where:
F is the magnitude of the force,
q is the charge of the particle (1.8 µC = 1.8 * 10^-6 C),
v is the speed of the particle (2.60 * 10^6 m/s),
B is the magnitude of the magnetic field (1.20 * 10^-3 T),
θ is the angle between the velocity vector and the magnetic field vector (which is 90 degrees since the particle is moving perpendicular to the fields).
Plugging in these values into the equation, we get:
F = (1.8 * 10^-6 C) * (2.60 * 10^6 m/s) * (1.20 * 10^-3 T) * sin(90°)
The sine of 90 degrees is equal to 1, so the equation simplifies to:
F = (1.8 * 10^-6 C) * (2.60 * 10^6 m/s) * (1.20 * 10^-3 T) * 1
Simplifying further, we have:
F = 6.768 * 10^-6 N
Therefore, the magnitude of the net force acting on the charge is 6.768 * 10^-6 N.
To determine the magnitude of the net force acting on the charge, we need to use the formula for the magnetic force experienced by a charged particle moving through a magnetic field and the formula for the electric force experienced by a charged particle in an electric field.
The magnetic force (F_m) experienced by a charged particle moving through a magnetic field is given by the equation:
F_m = q * v * B * sin(theta)
Where:
- q is the charge of the particle
- v is the velocity of the particle
- B is the magnetic field strength
- theta is the angle between the velocity vector and the magnetic field vector
In this case, the charged particle is moving perpendicular to the magnetic field, so the angle between the velocity vector and the magnetic field vector is 90 degrees. Thus, sin(theta) = 1.
The electric force (F_e) experienced by a charged particle in an electric field is given by the equation:
F_e = q * E
Where:
- q is the charge of the particle
- E is the electric field strength
In this case, the electric field and the magnetic field are pointing in the same direction, so their effects add up. Therefore, the net force (F_net) can be calculated by adding the magnitudes of the magnetic and electric forces:
F_net = |F_m| + |F_e|
Now, let's substitute the given values into the formulas:
|F_m| = |q * v * B * sin(theta)|
= |(1.8 * 10^(-6) C) * (2.60 * 10^6 m/s) * (1.20 * 10^(-3) T) * 1|
|F_e| = |q * E|
= |(1.8 * 10^(-6) C) * (5.50 * 10^3 N/C)|
Now, let's calculate the values:
|F_m| = (1.8 * 10^(-6) C) * (2.60 * 10^6 m/s) * (1.20 * 10^(-3) T) = 5.068 N
|F_e| = (1.8 * 10^(-6) C) * (5.50 * 10^3 N/C) = 9.9 * 10^(-3) N
Finally, summing up the magnitudes of the magnetic and electric forces gives us the magnitude of the net force:
F_net = |F_m| + |F_e| = 5.068 N + 9.9 * 10^(-3) N = 5.077 N
Therefore, the magnitude of the net force acting on the charge is 5.077 N.