The electric field due to a charged conducting sphere of radius 10 cm , at a distance of 20 cm from the centre of the sphere is 1.5*10pow3 NC-1 and points radially inwards.what is the charge on the sphere ?
To calculate the charge on the sphere, we can use Gauss's Law for the electric field.
Gauss's Law states that the electric flux through a closed surface is equal to the ratio of the total charge enclosed by the surface to the permittivity of free space (ε₀).
The electric field due to a conducting sphere can be considered to originate from a point-like charge located at the center of the sphere. Therefore, the electric field at any point outside the sphere is equal to the electric field that would be produced if all of the charge on the sphere were concentrated at its center.
In this case, we have the following information:
- Electric field (E) = 1.5 * 10^3 N/C
- Distance from the center of the sphere to the point where the electric field is measured (r) = 20 cm = 0.2 m
- Radius of the sphere (R) = 10 cm = 0.1 m
To find the charge (Q) on the sphere, we need to calculate the flux of the electric field through a Gaussian surface. A suitable Gaussian surface for this problem is a sphere centered at the center of the conducting sphere with a radius larger than the conducting sphere (let's call it R_gauss).
The electric flux (Φ) through our chosen surface is given by:
Φ = E * A = Q / ε₀,
where A is the area of the Gaussian surface.
For a Gaussian surface in the form of a sphere, the electric flux is given by:
Φ = E * 4πR_gauss^2
Since the electric field points radially inwards, the electric flux is negative:
Φ = -E * 4πR_gauss^2
Now, we can solve for Q by rearranging the equation:
Q = -Φ * ε₀ = -(-E * 4πR_gauss^2) * ε₀
Substituting the given values:
Q = -(1.5 * 10^3 N/C) * (4π * (0.2 m)^2) * ε₀
The value of ε₀ is the permittivity of free space, which is approximately 8.85 * 10^(-12) C^2/(N m^2).
Calculating the value of Q:
Q = -[(1.5 * 10^3 N/C) * (4π * (0.2 m)^2) * (8.85 * 10^(-12) C^2/(N m^2))]
After performing the calculations, the resulting value will give the charge (Q) on the sphere.