Question

A charged nonconducting rod, with a length of 3.00 m and a cross-sectional area of 3.02 cm2, lies along the positive side of an x axis with one end at the origin. The volume charge density p is charge per unit volume in coulombs per cubic meter. How many excess electrons are on the rod if p is (a) uniform, with a value of -5.51 uC/mº, and (b) nonuniform, with a value given by p = bx?, where b = -2.55 uC/m5?

(a) Number i ! Units No units
(b) Number i Units No units

Answer 1

To determine the number of excess electrons on a charged nonconducting rod, use the formula: number of excess electrons = volume charge density x volume of the rod. This can be done for both uniform and nonuniform charge densities.

Step-by-step explanation:

To find the number of excess electrons on the charged nonconducting rod, we need to use the formula:

Number of excess electrons = volume charge density (p) x volume of the rod (V)

(a) For the uniform charge density, we have p = -5.51 uC/m³. The volume of the rod is given by V = length x cross-sectional area. Substituting the values into the formula, we can calculate the number of excess electrons.

(b) For the nonuniform charge density, we have p = bx⁵, where b = -2.55 uC/m⁵ and x represents the distance along the rod. Using integration, we can find the volume of the rod and then calculate the number of excess electrons.