Consider a charged ring of radius 43.4 cm and total charge 18 nC.
We are interested in the electric field a perpendicular distance z away from the center of the ring.
At what distance from the center of the ring does the electric field become maximum?
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/ElectricForce/Axis-of-Loop.html
To find at what distance from the center of the ring the electric field becomes maximum, we need to determine the equation for the electric field at a point on the perpendicular axis passing through the center of the ring.
The electric field due to a charged ring at a perpendicular distance (z) away from the center can be calculated using the following equation:
E = k * (Q * z) / (2 * π * ε * (z^2 + r^2)^1.5)
where:
- E is the electric field at the point,
- k is Coulomb's constant (9 × 10^9 N*m²/C²),
- Q is the total charge on the ring (18 nC = 18 × 10^(-9) C),
- z is the perpendicular distance from the center of the ring,
- r is the radius of the ring (43.4 cm = 0.434 m),
- ε is the permittivity of free space (8.854 × 10^(-12) C²/N*m²).
The expression (z^2 + r^2)^1.5 represents the distance between the point and the ring to the power of 1.5. This accounts for the inverse square law behavior of the electric field.
To find the distance from the center of the ring where the electric field is maximum, we need to differentiate the equation for the electric field with respect to z and find the value of z when the derivative is zero. This will give us the critical point, which in this case corresponds to the maximum of the electric field.
However, since the equation for the electric field is quite complex, we can solve it numerically using a computer program or mathematical software. By substituting the given values into the equation, we can find the distance from the center of the ring where the electric field is maximum.