An electric field of 2.04 kV/m and a magnetic field of 0.548 T act on a moving electron to produce no net force. If the fields are perpendicular to each other, what is the electron's speed?
Require that the magnetic and electrical forces be equal.
e*V*B = e*E
The charge, e, cancels out, so
V = (E/B)
If E is in V/m (NOT kV/m), and B is in Tesla, the answer will be in m/s.
V = 2040/0.548 = ?
To find the electron's speed, we can use the fact that there is no net force acting on the electron in this scenario. Since the electric field and the magnetic field are perpendicular to each other, they exert forces in different directions.
The force due to the electric field can be calculated using the formula: F_electric = q * E, where F_electric is the force, q is the charge of the electron, and E is the electric field strength.
Similarly, the force due to the magnetic field can be calculated using the formula: F_magnetic = q * v * B, where F_magnetic is the force, q is the charge of the electron, v is the velocity of the electron, and B is the magnetic field strength.
Since the net force is zero, we can equate the electric field force with the magnetic field force:
F_electric = F_magnetic
q * E = q * v * B
q cancels out on both sides of the equation:
E = v * B
We can rearrange the equation to solve for the velocity v:
v = E / B
Now we can substitute the given values:
v = 2.04 kV/m / 0.548 T
Before we can proceed, we need to convert kV/m to V/m and T to tesla:
1 kV/m = 1000 V/m
1 T = 1 tesla
v = (2.04 × 1000 V/m) / 0.548 T
v = 2.04 × 1000 / 0.548 m/s
v ≈ 3722.63 m/s
Therefore, the electron's speed is approximately 3722.63 m/s.