A circular disk of 10cm radius is charged uniformly with a total charge of Q. Find the electric field intensity at a point 20cm away from the disk along its axis
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To find the electric field intensity at a point along the axis of a charged disk, we can use the equation for electric field due to a uniformly charged disk:
E = (σ / 2ε₀) * (1 - (z / √(R² + z²)))
Where:
E is the electric field intensity at the point along the axis
σ is the surface charge density of the disk
ε₀ is the vacuum permittivity (8.85 x 10⁻¹² C²/Nm²)
z is the distance between the point and the center of the disk along the axis
R is the radius of the disk
In this case, the disk has a radius of 10 cm (0.1 m) and is uniformly charged with a total charge of Q. To find the surface charge density σ, we divide the total charge by the area of the disk:
σ = Q / A
The area of a circular disk is given by A = πR². Substituting the values, we get:
σ = Q / (π * R²)
Next, we substitute the values of σ, R, z, and ε₀ into the electric field equation:
E = (σ / 2ε₀) * (1 - (z / √(R² + z²)))
E = (Q / (2πε₀ * R²)) * (1 - (z / √(R² + z²)))
Now we can plug in the values and calculate the electric field intensity:
E = (Q / (2π * (8.85 x 10⁻¹² C²/Nm²) * (0.1 m)²)) * (1 - (0.2 m / √((0.1 m)² + (0.2 m)²)))
Simplifying this expression will give us the electric field intensity at the given point along the axis.