To find the value of the electric field intensity at a point between two concentric spheres, we can use Gauss's law.
Step 1: Define the problem
Let's assume that we have two concentric spheres, with the larger sphere having a radius of R1 and the smaller sphere having a radius of R2. We want to find the electric field intensity at a point P located between the two spheres.
Step 2: Understand Gauss's law
Gauss's law states that the total electric flux through any closed surface is proportional to the total charge enclosed by that surface. Mathematically, it can be written as:
Φ = ε₀ * Q_enclosed
Where Φ is the electric flux, ε₀ is the permittivity of free space, and Q_enclosed is the total charge enclosed by the closed surface.
Step 3: Choose a Gaussian surface
In this case, we can choose a spherical Gaussian surface with a radius r between R1 and R2. This spherical surface will enclose only the smaller sphere.
Step 4: Determine the enclosed charge
Since the smaller sphere is enclosed by our chosen Gaussian surface, the enclosed charge (Q_enclosed) will be the charge on the smaller sphere. Let's denote this charge as Q2.
Step 5: Calculate the electric field intensity
Since the surface is spherical and the charge is concentrated at the center of the sphere, the electric field intensity will be constant and radially outward in direction. Using Gauss's law, we can write:
Φ = ε₀ * Q2
The electric flux through the surface can be expressed as:
Φ = E * 4πr²
where E is the electric field intensity at the point P and r is the radius of the Gaussian surface (between R1 and R2).
Combining the above equations, we get:
E * 4πr² = ε₀ * Q2
Finally, we can solve for the electric field intensity E:
E = (ε₀ * Q2) / (4πr²)
Step 6: Substitute values and calculate
Substitute the values of ε₀, Q2, and r into the equation to get the electric field intensity at point P.
It's important to note that the electric field intensity will change if the point P is located either inside or outside the smaller sphere.