A charge of 1nC is added to a spherical soap bubble with a radius of 3.0cm.
What is the electric field strength just outside of the bubble?
What is the electric field strength just inside of the bubble?
The field experienced by each charge in the skin of the bubble is the average of the field strength just inside and the field just outside of the bubble. Given this, what outward pressure (in N/m^2) is exerted on the bubble as a result of it being charged?
Wouldn't you use Gauss Law for this?
Inside, zero, no charge is contained.
Pressure=force/area=Eq/area=E*surface charge density.
= Eq/areabubble
To calculate the electric field strength just outside of the bubble, we can use Coulomb's Law. Coulomb's Law states that the electric field strength (E) at a point in space is equal to the force (F) experienced by a unit positive charge at that point divided by the magnitude of the charge (q).
We know that the charge q added to the spherical soap bubble is 1nC (1 nanocoulomb), and the radius of the bubble is 3.0cm.
The formula for the electric field strength just outside a charged sphere is given by:
E = k * (Q / r^2)
Where:
E is the electric field strength outside the sphere
k is the Coulomb's constant (approximately 9 x 10^9 Nm^2/C^2)
Q is the charge on the sphere
r is the radius of the sphere
Substituting the given values, we have:
E = (9 x 10^9 Nm^2/C^2) * (1 x 10^-9 C) / (0.03m)^2
Calculating this, we get:
E = 3 x 10^6 N/C
Therefore, the electric field strength just outside the spherical soap bubble is 3 x 10^6 N/C.
To calculate the electric field strength just inside the bubble, we need to consider that the electric field inside a uniformly charged sphere is zero. This is because the electric field from all the charged particles cancel each other out due to symmetry. Therefore, the electric field strength inside the bubble is zero.
Now, let's calculate the outward pressure exerted on the bubble due to its charge.
The outward pressure exerted on the bubble can be determined using the following formula:
Pressure = (2 * E^2 * ε0) / 3
Where:
E is the electric field strength just outside the bubble
ε0 is the permittivity of free space (approximately 8.85 x 10^-12 F/m)
Substituting the values, we have:
Pressure = (2 * (3 x 10^6 N/C)^2 * (8.85 x 10^-12 F/m)) / 3
Calculating this, we get:
Pressure ≈ 5.31 N/m^2
Therefore, the outward pressure exerted on the spherical soap bubble as a result of it being charged is approximately 5.31 N/m^2.