Electrons move at a speed of 4.4 104 m/s through a 6.0 10-2 T magnetic field which is perpendicular to their motion. Calculate the radius of the electrons' circular path.
To calculate the radius of the electrons' circular path, we can use the formula for the magnetic force on a charged particle moving in a magnetic field:
F = (e)(v)(B)
Where:
F is the magnetic force,
e is the charge of the electron (1.6 × 10^-19 C),
v is the velocity of the electron (4.4 × 10^4 m/s),
B is the magnetic field strength (6.0 × 10^-2 T).
The magnetic force acting on the electron provides the centripetal force necessary to keep it in circular motion. The centripetal force can be calculated using the formula:
F = (m)(a)
Where:
F is the centripetal force,
m is the mass of the electron (9.1 × 10^-31 kg), and
a is the centripetal acceleration.
Since the centripetal acceleration is given by a = v²/r, where r is the radius of the circular path, we can substitute this value into the equation:
F = (m)(v²/r)
Since the magnetic force (F) is equal to the centripetal force, we can equate the two expressions:
(m)(v²/r) = (e)(v)(B)
By rearranging the equation, we can solve for the radius (r):
r = (m)(v)/(e)(B)
Now, let's substitute the given values into the equation to calculate the radius.