A spherical conductor has a radius of 14.0 cm and charge of 26.0 µC. Calculate the electric field and the electric potential (a) r = 10.0 cm, (b) r = 20.0 cm, and (c) r = 14.0 cm from the center.
how do i calculate k?
k is the Coulomb's-law constant, which appears in the formula you need to use, you look it up. It is a constant of nature.
(a) there is no E-field indide the conductor. The potential there is the value at the surface, which equals
-kQ/R
where R is the sphere radius, 0.14 m, and Q is the charge on the sphere.
(b) and (c): Your turn
To calculate the value of k, you need to use Coulomb's law, which relates the electric force between two charged objects to the distance between them and their charges. Coulomb's law is given by the equation:
F = k * (q1 * q2) / r^2
where F is the electric force between two objects, q1 and q2 are the charges of the objects, r is the distance between the centers of the objects, and k is the proportionality constant.
The value of k depends on the choice of units. In the SI (International System of Units), the value of k is approximately 9.0 x 10^9 N m^2/C^2.
So, to calculate k, you divide the electric force by the product of the charges and the square of the distance between them:
k = F * r^2 / (q1 * q2)
For example, if you know the electric force between two charges, the distances between them, and the charges themselves, you can use this equation to find the value of k.
To calculate the electric field and electric potential at different distances from a charged spherical conductor, we need to use Coulomb's Law and the equation for electric potential.
1. Coulomb's Law:
Coulomb's Law states that the electric field (E) created by a point charge is given by the equation: E = k * (q/r^2), where E is the electric field, k is Coulomb's constant (9.0 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the center of the conductor.
2. Equation for Electric Potential:
The electric potential (V) created by a charged object is given by the equation: V = k * (q/r), where V is the electric potential.
To find the constant k in these equations, we need to know the value of Coulomb's constant, which is approximately 9.0 x 10^9 Nm^2/C^2.