A particle with a charge of -4.0x10^-5 C, a mass of 2.0x10^-7 kg and a velocity of 6.0x10^4 m/s [W] is travelling perpendicularly through an external magnetic field such that the force of gravity is balanced by the magnetic force. Determine the direction and magnitude of the external force. Ignore any effect due to the Earth's magnetic field
To determine the direction and magnitude of the external force on the particle, we can use the equation that relates the force on a charged particle moving through a magnetic field.
The equation for the magnetic force on a charged particle is given by:
F = qvBsinθ
where:
- F is the force on the particle (in newtons),
- q is the charge of the particle (in coulombs),
- v is the velocity of the particle (in meters per second),
- B is the magnetic field strength (in teslas), and
- θ is the angle between the velocity vector and the magnetic field vector.
Given:
- q = -4.0x10^-5 C (charge of the particle)
- m = 2.0x10^-7 kg (mass of the particle)
- v = 6.0x10^4 m/s (velocity of the particle)
- θ = 90 degrees (since the particle is moving perpendicularly to the magnetic field)
First, we need to calculate the magnetic field strength (B) using the equation of equating gravitational force and magnetic force:
mg = qvB
Rearranging the equation, we can solve for B:
B = mg / (qv)
Substituting the given values:
B = (2.0x10^-7 kg) * (9.8 m/s^2) / (-4.0x10^-5 C * 6.0x10^4 m/s)
Simplifying the expression gives:
B ≈ 8.17x10^-3 T (teslas)
Now that we have the value of B, we can calculate the magnitude of the external force (F) on the particle using the formula:
F = qvBsinθ
Plugging in the values:
F = (-4.0x10^-5 C) * (6.0x10^4 m/s) * (8.17x10^-3 T) * sin(90 degrees)
Simplifying the expression gives:
F ≈ 1.96 N (newtons)
Therefore, the magnitude of the external force on the particle is approximately 1.96 newtons.
Since the particle has a negative charge, the force will be in the opposite direction of the magnetic field. However, since we are not given the direction of the magnetic field, we cannot determine the exact direction of the external force without this information.