A circular disk of 10cm radius is charged uniformly with a total charge of Q coul.find the electric field intensity at a point 20cm away from the disk,along its axis
To find the electric field intensity at a point 20 cm away from the disk along its axis, we can use the formula for the electric field due to a uniformly charged disk.
The formula for the electric field intensity at a point on the axis of a uniformly charged disk is:
E = (σ / 2ε₀) * (1 - (z / √(z² + R²)))
Where:
E is the electric field intensity
σ is the surface charge density (charge per unit area) of the disk
ε₀ is the permittivity of free space
z is the distance from the center of the disk to the point on the axis
R is the radius of the disk
In this case, we are given that the radius of the disk is 10 cm, which is equivalent to 0.1 m.
First, we need to calculate the surface charge density (σ). The charge per unit area is given by:
σ = Q / A
Where:
Q is the total charge of the disk
A is the area of the disk
The area of a circle is given by:
A = π R²
Now, we can substitute the values into the formula to find the electric field intensity (E) at the given distance (z = 20 cm):
E = (σ / 2ε₀) * (1 - (z / √(z² + R²)))
E = (Q / (2ε₀ π R²)) * (1 - (z / √(z² + R²)))
E = (Q / (2ε₀ π (0.1 m)²)) * (1 - (0.2 m / √((0.2 m)² + (0.1 m)²)))
Finally, calculate the electric field intensity (E) using the given value of Q:
E = (Q / (2ε₀ π (0.1 m)²)) * (1 - (0.2 m / √((0.2 m)² + (0.1 m)²)))
Please note that ε₀ is the permittivity of free space, which has a value of approximately 8.85 x 10⁻¹² C²/(N·m²). Substitute this value to get the final answer.
I hope this explanation helps! Let me know if you need any further assistance.