A circular rod has a radius of curvature R = 9.09 cm and a uniformly distributed positive charge Q = 6.49 pC and subtends an angle θ = 2.59 rad. What is the magnitude of the electric field that Q produces at the center of curvature?

E = 1.19 N/C

Explanation:

Let's first determine the length of the arc which can be given as:

L= Rθ

where:

L = length of the arc

R = radius of curvature

θ = angle in radius

L = (9.09×10⁻²m)(2.59)

L = (0.0909)(2.59)

L = 0.235431 m

Then, the magnitude of electric field that Q produces at the center of curvature can be calculated by using the formula:

Since

where;

L = length

Q = charge

λ =  density of the charge;

then substituting for λ, we have :

substituting our given parameter; we have:

E = 1.1889 N/C

E = 1.19 N/C

∴ the magnitude of the electric field that Q produces at the center of curvature = 1.19 N/C

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.