In Figure 20.2 is a velocity selector that can be used to measure the speed of a charged particle. A beam of particles is directed along the axis of the instrument. A parallel plate capacitor sets up an electric field E which is oriented perpendicular to a uniform magnetic field B. If the plates are separated by 3 mm and the value of the magnetic field is 0.3 T, what voltage between the plates will allow particles of speed to pass straight through without deflection
To determine the voltage between the plates that will allow particles of a certain speed to pass straight through the velocity selector without deflection, we need to understand the relationship between the electric and magnetic fields.
In this case, the particles are moving along the axis of the instrument, which means they are moving in a particular direction. The electric field (E) is oriented perpendicular to the uniform magnetic field (B), which means they are at right angles to each other.
When a charged particle moves through a magnetic field, it experiences a force, which can cause it to deviate from its original path. However, if the force experienced by the particle due to the magnetic field is equal and opposite to the force experienced due to the electric field, the net force on the particle will be zero. This will result in the particle moving straight through without deviation.
The force experienced by a charged particle moving through a magnetic field is given by the equation:
F = q*v*B
Where q is the particle's charge, v is its velocity, and B is the magnetic field strength.
The force experienced by a charged particle due to the electric field in a capacitor is given by the equation:
F = q*E
Where E is the electric field strength.
To achieve no deflection, we can set up the equation:
Fmagnetic = Felectric
q*v*B = q*E
We can simplify this equation by canceling out the charge (q) on both sides:
v*B = E
Now we can solve for the electric field (E) by rearranging the equation:
E = v*B
The electric field in a capacitor is related to the voltage (V) between the plates and the distance (d) between them by the equation:
E = V / d
Combining these equations, we have:
V / d = v*B
Rearranging this equation, we can solve for the voltage (V):
V = v*B*d
Substituting the given values into the equation, we have:
V = ( speed * magnetic field * distance )
Plug in the values of speed (given in the question), magnetic field (0.3 T), and distance (3 mm = 0.003 m) to get the value of voltage (V) that will allow particles of that speed to pass straight through without deflection.