An electron oscillates one thousand million times per second along the z-axis with a displacement z(t)=sin(ωt) mm. What is the value of the electric fie
ld E(t) produced at a distance r of ten meters (x=10m, y=0, z=0)?
The Feynman Lectures :
Ez(x)=kq/rc^2 (a(t-x/c)) where a is the acceleration of the charge, an c is the speed of light, k=1/4PIepislion)
acceleration:
z=sin(wt)
v=wcos(wt)
a=w^2sin(wt) in MKS, a=.001w^2sinwt m/s^2
c look it up.
q is charge on one electron, in coulombs.
Is this enough?
I don't know how can I calculate the acceleration if I don't have the time, or it must depend on t? The whole Ez(x) equation?
Thanks
You think this is right?
imgur(dot)com/iijkycf(dot)jpg
Thank you
To find the value of the electric field E(t) produced at distance r = 10 meters (x = 10m, y = 0, z = 0), we can use Coulomb's law.
Coulomb's law states that the electric field E at a point due to a charged particle is given by:
E = k * (q / r^2)
where k is the Coulomb's constant (k ≈ 9 × 10^9 Nm^2/C^2), q is the charge of the particle, and r is the distance from the charged particle to the point where the electric field is being calculated.
In this case, we are dealing with an electron, which has a charge of approximately -1.6 × 10^(-19) Coulombs.
Now, we need to determine the value of q, the charge of the electron, based on the given information about its motion. The displacement z(t) of the electron along the z-axis at time t is given by:
z(t) = sin(ωt) mm
where ω represents the angular frequency of the oscillation. The angular frequency ω can be calculated using the formula:
ω = 2πf
where f is the frequency of oscillation. In this case, the frequency is given as one thousand million times per second, which is equivalent to 10^9 Hz. Therefore:
ω = 2π * (10^9)
≈ 6.283 × 10^9 rad/s
Now, let's substitute the value of ω and the displacement z(t) into the equation to find the charge q:
z(t) = sin(ωt) mm
q = z(t) * (2 * 10^-3) * 1.6 × 10^(-19)
= sin(ωt) * (2 * 10^-3) * 1.6 × 10^(-19)
where (2 * 10^-3) is used to convert the displacement from mm to meters.
After calculating the value of q, we can find the electric field E(t) at distance r = 10 meters using Coulomb's law:
E(t) = k * (q / r^2)
= (9 × 10^9) * (q / (10^2))
≈ (9 × 10^9) * (q / 100)
Finally, you can substitute the calculated value of q into the equation to find the value of the electric field E(t) produced at distance r = 10 meters.