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)?
To determine the value of the electric field E(t) produced at a distance of ten meters from the electron along the x-axis, we can use Coulomb's law. Coulomb's law states that the electric field at a point in space is proportional to the charge and inversely proportional to the square of the distance from the source of the field.
Given:
- Charge of an electron (q) = -1.6 × 10^-19 C
- Distance from the source (r) = 10 m
The electric field E(t) produced by the electron at a distance of ten meters can be calculated using the formula:
E(t) = (k * q) / r^2
where:
- k is the Coulomb's constant, approximately 9 × 10^9 Nm^2/C^2
- q is the charge of the electron
- r is the distance from the source
Substituting the known values:
E(t) = (9 × 10^9 Nm^2/C^2 * (-1.6 × 10^-19 C)) / (10 m)^2
E(t) = -14.4 × 10^-10 N/C
Therefore, the value of the electric field E(t) at a distance of ten meters from the electron is approximately -14.4 × 10^-10 N/C.
To find the value of the electric field (E(t)) produced at a distance r of ten meters from the electron, we can use Coulomb's law, which states that the electric field produced by a point charge is given by the equation:
E = (k * q) / r^2
Where:
- E is the electric field
- k is Coulomb's constant (8.99 x 10^9 N m^2/C^2)
- q is the charge of the electron (1.60 x 10^-19 C, which is the elementary charge)
- r is the distance between the electron and the point where we want to measure the electric field.
In this case, we are given that the electron is oscillating along the z-axis with a displacement z(t) = sin(ωt) mm, where ω represents the angular frequency of the oscillation.
To find the electric field at a distance of ten meters (r = 10m) with respect to the z-axis, we need to convert the sinusoidal displacement from millimeters to meters.
Given that 1 mm = 0.001 m, we have:
z(t) = sin(ωt) * 0.001 m
Now, we can substitute the value of z(t) into the equation for the electric field:
E(t) = (k * q) / r^2
Note that the charge (q) of an electron remains constant, so we don't need to consider the time dependence of the charge.
Therefore, plugging in the values:
E(t) = (8.99 x 10^9 N m^2/C^2 * 1.60 x 10^-19 C) / (10m)^2
Simplifying the equation:
E(t) = (1.44 x 10^-9 N m^2/C) / 100 m^2
E(t) = 1.44 x 10^-11 N/C
Thus, the value of the electric field (E(t)) produced at a distance of ten meters from the electron along the z-axis is 1.44 x 10^-11 N/C.