An electron moving parallel to the x axis has an initial speed of 4.82 *10^6 m/s at the origin. Its speed is reduced to 1.46 * 10^5 m/s at the point x = 2.00 cm.
Calculate the electric potential difference between the origin and that point.
To calculate the electric potential difference between the origin and the given point, we can use the concept of electric potential energy.
The change in electric potential energy (ΔPE) of a charged particle moving in an electric field is given by the equation:
ΔPE = qΔV
where ΔV is the change in electric potential and q is the charge of the particle. In this case, the charge of an electron is -1.6 * 10^-19 C.
To find the change in electric potential, we need to first calculate the initial and final electric potentials separately and then subtract them.
1. Calculate the initial electric potential (V_i):
The initial electric potential energy (PE_i) can be calculated using the formula:
PE_i = 0.5 * mv_i^2
where m is the mass of the electron and v_i is the initial velocity of the electron.
The mass of an electron (m) is 9.11 * 10^-31 kg.
PE_i = 0.5 * (9.11 * 10^-31 kg) * (4.82 * 10^6 m/s)^2
2. Calculate the final electric potential (V_f):
The final electric potential energy (PE_f) can be calculated using the formula:
PE_f = 0.5 * mv_f^2
where v_f is the final velocity of the electron.
PE_f = 0.5 * (9.11 * 10^-31 kg) * (1.46 * 10^5 m/s)^2
3. Calculate the change in electric potential (ΔV):
ΔV = (PE_f - PE_i) / q
where q is the charge of the electron.
ΔV = (PE_f - PE_i) / (-1.6 * 10^-19 C)
4. Convert the change in electric potential to volts:
1 volt = 1 joule / 1 coulomb
So, multiply the value of ΔV by the conversion factor (1 V / 1 J).
The result will be the electric potential difference between the origin and the given point.