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Explain Bot To determine the strength of the magnetic field experienced by the electron, we need to use the formula for the radius of a circular path of a charged particle in a magnetic field.
The formula is given as:
r = (mv) / (Bq)
Where:
- r is the radius of the circular path
- m is the mass of the charged particle
- v is the velocity of the charged particle
- B is the magnetic field strength
- q is the charge of the particle
We are given the following information:
- The radius of the circular path (r) is 4.0 cm, which is equal to 0.04 m.
- The electron is accelerated by 5.2 kV, which implies a voltage (V) of 5.2 kV, or 5200 V.
- The charge of an electron (q) is -1.6 x 10^(-19) C (coulombs).
To find the velocity (v) of the electron, we can use the relationship between voltage and velocity in an electron beam:
V = mv^2 / 2q
Rearranging the equation to isolate v:
v = sqrt(2qV / m)
The mass of an electron (m) is approximately 9.11 x 10^(-31) kg.
Plugging in the values:
v = sqrt((2)(-1.6 x 10^(-19) C)(5200 V) / (9.11 x 10^(-31) kg))
Calculating the value of v:
v ≈ 5.68 x 10^6 m/s
Now that we have the radius (r) and the velocity (v), we can rearrange the equation for the radius of a circular path to find the magnetic field strength (B).
B = (mv) / (rq)
Plugging in the values:
B = ((9.11 x 10^(-31) kg)(5.68 x 10^6 m/s)) / ((0.04 m)(-1.6 x 10^(-19) C))
Calculating the value of B:
B ≈ 7.17 x 10^(-4) T (Tesla)
Therefore, the electron must experience a magnetic field strength of approximately 7.17 x 10^(-4) T to create a circular path with a radius of 0.04 m.