You have arranged that the magnetic field in a particular region of space is due North with a value of 0.009 T. An electron enters the field traveling to the west with a speed of 0.09 of the speed of light. As a result, the electron experiences a magnetic force, which is upward. What is the strength of this magnetic force, in fN? The "f" here stands for "femto", which is 10-15.
To find the strength of the magnetic force experienced by the electron, we can use the magnetic force equation:
F = q * v * B * sin(theta)
where:
F is the magnetic force,
q is the charge of the particle (in this case, the charge of an electron: -1.6 x 10^-19 C),
v is the velocity of the particle (0.09c),
B is the magnetic field strength (0.009 T),
and theta is the angle between the velocity vector and the magnetic field vector (90 degrees, since the force is perpendicular to both).
Plugging in the given values, we have:
F = (-1.6 x 10^-19 C) * (0.09c) * (0.009 T) * sin(90°)
Since sin(90°) = 1, we can simplify this to:
F = (-1.6 x 10^-19 C) * (0.09c) * (0.009 T)
Using the value for the charge of an electron (-1.6 x 10^-19 C) and the speed of light (c ≈ 3 x 10^8 m/s), we can calculate the magnetic force:
F = (-1.6 x 10^-19 C) * (0.09) * (0.009 T)
F = -1.296 x 10^-29 N
The negative sign indicates that the force is directed in the opposite direction of the initial velocity vector, which in this case is upward.
To convert this force to femtonewtons (fN), you need to multiply by 10^15:
F_fN = (-1.296 x 10^-29 N) * (10^15 fN / 1 N)
F_fN ≈ -1.3 fN
Therefore, the strength of the magnetic force experienced by the electron is approximately 1.3 femtonewtons (fN) upward.