A spherical metal dome of radius 15 cm is electrically charged. It has a positive charge of +2.5 μC distributed uniformly on its surface.
a. Calculate the electric field strength on the surface of the dome.
b. Explain how your answer to a would change at a distance of 30 cm from the surface of the dome.
a)
1000000 v/m
a. To calculate the electric field strength on the surface of the dome, we can use the formula for electric field due to a uniformly charged sphere. The formula is given as:
E = k * Q / r^2
where E is the electric field strength, k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2), Q is the charge on the sphere, and r is the radius of the sphere.
In this case, the charge on the sphere is Q = +2.5 μC = +2.5 x 10^-6 C.
The radius of the sphere is r = 15 cm = 0.15 m.
Substituting these values into the formula, we get:
E = (9 x 10^9 Nm^2/C^2) * (+2.5 x 10^-6 C) / (0.15 m)^2
E = (9 x 10^9 Nm^2/C^2) * (2.5 x 10^-6 C) / (0.0225 m^2)
E = 3 x 10^6 N/C
Therefore, the electric field strength on the surface of the dome is 3 x 10^6 N/C.
b. At a distance of 30 cm from the surface of the dome, the electric field strength would change. The electric field strength due to a point charge decreases as the distance from the charge increases. Since the sphere is uniformly charged and we are outside the sphere, we can assume the charge is concentrated at the center of the sphere.
To calculate the electric field strength at this distance, we can use the same formula:
E = k * Q / r^2
where E is the electric field strength, k is the electrostatic constant, Q is the charge on the sphere (which remains the same), and r is the distance from the center of the sphere.
In this case, the charge on the sphere is Q = +2.5 μC = +2.5 x 10^-6 C.
The distance from the center of the sphere is r = 30 cm = 0.3 m.
Substituting these values into the formula, we get:
E = (9 x 10^9 Nm^2/C^2) * (+2.5 x 10^-6 C) / (0.3 m)^2
E = (9 x 10^9 Nm^2/C^2) * (2.5 x 10^-6 C) / (0.09 m^2)
E ≈ 7.5 x 10^5 N/C
Therefore, the electric field strength at a distance of 30 cm from the surface of the dome is approximately 7.5 x 10^5 N/C.
To calculate the electric field strength on the surface of the dome, we can use the formula for electric field due to a point charge:
Electric field strength (E) = k * (q / r^2)
where:
- E is the electric field strength
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
- q is the charge
- r is the distance from the charged object
In this case, the charge (q) is +2.5 μC = 2.5 x 10^-6 C, and the radius (r) is 15 cm = 0.15 m.
a. Calculate the electric field strength on the surface of the dome:
Plugging the values into the formula, we get:
E = (9 x 10^9 Nm^2/C^2) * (2.5 x 10^-6 C / (0.15)^2 m^2)
Simplifying the expression, we find:
E ≈ 3 x 10^5 N/C
Therefore, the electric field strength on the surface of the dome is approximately 3 x 10^5 N/C.
b. To determine how the electric field strength changes at a distance of 30 cm from the surface of the dome, we need to calculate the electric field strength at that distance using the same formula.
At a distance of 30 cm = 0.30 m from the surface of the dome, the new radius (r) is 0.15 m + 0.30 m = 0.45 m.
Plugging the values into the formula, we have:
E = (9 x 10^9 Nm^2/C^2) * (2.5 x 10^-6 C / (0.45)^2 m^2)
Simplifying the expression, we find:
E ≈ 4 x 10^4 N/C
Therefore, at a distance of 30 cm from the surface of the dome, the electric field strength is approximately 4 x 10^4 N/C.
In summary, the electric field strength decreases significantly as the distance from the surface of the dome increases. At the surface, it is approximately 3 x 10^5 N/C, but at a distance of 30 cm, it decreases to approximately 4 x 10^4 N/C.
a) From formula V=KQ/R and E=QV
We get E =KQ^2/R=(1.38×10^-23×(2.5×10^-6)^2)/0.15
E=5.75×10^-34 Vm^-1