The maximum electric field intensity on the axis of a uniformly charged ring of charge q and radius R will be

• 1/(4πε₀) * (q/(R² + z²)^(3/2))
• 2q/(3R²)
• 1/(4πε₀) * (2q/(R² + z²)^(3/2))
• 3q/(2√2R²)

The maximum electric field intensity along the axis of a uniformly charged ring can be derived from the formula for the electric field due to a ring of charge. The expression for the electric field intensity \( E \) at a distance \( z \) from the center of the ring along its axis is given by:

Electric Field Formula

The formula is:

E(z) = \frac{1}{4\pi \epsilon_0} \cdot \frac{q \cdot z}{(R^2 + z^2)^{3/2}}

Finding the Maximum Electric Field

To find the maximum electric field, we need to differentiate this expression with respect to \( z \) and set the derivative to zero. This will help us locate the point where the electric field is at its peak.

Key Points

• The maximum electric field occurs at a specific distance from the ring.
• For a uniformly charged ring, the maximum electric field intensity can be simplified to:
• E_{max} = \frac{2q}{3R^2} \cdot \frac{1}{4\pi \epsilon_0}

Thus, the maximum electric field intensity on the axis of a uniformly charged ring is given by the expression:

E_{max} = \frac{2q}{3R^2} \cdot \frac{1}{4\pi \epsilon_0}

This result shows how the charge and radius of the ring influence the electric field intensity at its maximum point along the axis.