Thank you !
At some instant the velocity components of an electron moving between two charged parallel plates are vx = 1.3 105 m/s and vy = 3.6 103 m/s. Suppose that the electric field between the plates is given by E = (120 N/C) j.
(a) What is the electron's acceleration in the field?
m/s2 j
(b) What is the electron's velocity when its x coordinate has changed by 4.8 cm?
m/s i + m/s j
(a) The acceleration can only be in the direction between the plates, and equals
a = F/m, where the force is F = e E
e is the electron charge.
a = (e/m) E.
m is the mass of an electron.
Look up m and e and solve for a.
(b) The velocity component parallel to the plates remains constant. You don't say whether the plates are oriented in the x or y direction; that needs to be specified. The velocity component between the plates changes from v1 to v2 according to
(1/2)(v2^2 - v1^2) = e E *(change in x)
In your case the change in x is 0.048 m.
Thanx!!!!
I left out the mass in one equation. it should read:
The velocity component between the plates changes from v1 to v2 according to
(1/2)(v2^2 - v1^2) = a *(change in x)
= (e/m) E *(change in x)
To solve part (a) of the problem, we need to find the acceleration of the electron in the electric field. The formula for acceleration is given by a = F/m, where F is the force experienced by the electron and m is the mass of the electron. In this case, the force is given by F = eE, where e is the charge of the electron and E is the electric field between the plates.
To find the acceleration, we need to know the values of e and m. The charge of an electron is a fundamental value and is approximately equal to -1.6 x 10^-19 Coulombs. The mass of an electron is also a fundamental value and is approximately equal to 9.1 x 10^-31 kilograms.
Now we can substitute the values into the equation a = (e/m)E.
a = (-1.6 x 10^-19 C) / (9.1 x 10^-31 kg) * (120 N/C) j
Simplifying the expression, we get:
a = -2.09 x 10^11 m/s^2 j
Therefore, the electron's acceleration in the field is approximately -2.09 x 10^11 m/s^2 in the j direction.
Now, let's move on to part (b) of the problem. We are asked to find the electron's velocity when its x coordinate has changed by 4.8 cm.
The formula to use here is (1/2)(v2^2 - v1^2) = a * (change in x), where v1 is the initial velocity in the x direction, v2 is the final velocity in the x direction, a is the acceleration, and (change in x) is the change in position in the x direction.
In this case, we know that the change in x is 0.048 m, so we can plug in the values into the equation:
(1/2)(v2^2 - v1^2) = (-2.09 x 10^11 m/s^2) * (0.048 m)
Simplifying the expression, we get:
(v2^2 - v1^2) = -2.5092 x 10^10 m^2/s^2
We need to solve for v2, so let's rearrange the equation:
v2^2 = v1^2 - 2.5092 x 10^10 m^2/s^2
Taking the square root of both sides, we get:
v2 = sqrt(v1^2 - 2.5092 x 10^10 m^2/s^2)
Substituting the given value of v1 (vx = 1.3 x 10^5 m/s), we get:
v2 = sqrt((1.3 x 10^5 m/s)^2 - 2.5092 x 10^10 m^2/s^2)
Calculating the value, we find that:
v2 ≈ 1.2999 x 10^5 m/s
Therefore, the electron's velocity when its x coordinate has changed by 4.8 cm is approximately 1.2999 x 10^5 m/s in the i direction.