Charge and excess electrons in a rod

In summary, the problem involves a charged nonconducting rod of length 3.00 m and cross-sectional area of 5.37 cm2 lying along the positive side of an x-axis. The volume charge density ρ is given as -2.54 µC/m3 for a uniform charge distribution and as ρ = bx2 with b = -1.36 µC/m5 for a nonuniform charge distribution. To find the number of excess electrons, the charge q is calculated using the equation q = p * (pi) * r2 * L, and then dividing by the charge of an electron. For the nonuniform distribution, the integral is used to find the charge q and then divided by the charge of an
  • #1
nothingatall
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0

Homework Statement



A charged nonconducting rod, with a length of 3.00 m and a cross-sectional area of 5.37 cm2, lies along the positive side of an x-axis with one end at the origin. The volume charge density ρ is charge per unit volume in coulombs per cubic meter. How many excess electrons are on the rod if ρ is (a) uniform, with a value of -2.54 µC/m3, and (b) nonuniform, with a value given by ρ = bx2, where b = -1.36 µC/m5?


Homework Equations


F=kQq/r^2
q=volume charge density*area of circle*length




The Attempt at a Solution


q=p*(pi)r^2*L=-2.54e-6C/m^3*5.37cm^2*3.00m=-4.09e-9
q/e=-4.09e-9/-1.6e-19=2.6e10e<--this was correct

part b: p=bx^2=-1.36e-6x^2
dq=Apdx
dq=5.37e-4*-1.36e-6x^2 dx
did the integral procedure and it may be wrong:
integral(dq)=7.3032e-10 *integral (x^2) from 0 to 2 =-1.94e-9
q/e=-1.94e-9/-1.6e-19 = 1.22e10<-- marked incorrect

I don't know how to fix this.
 
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  • #2
Why did to integrate from 0 to 2 if the length of the rod is 3 m?
 
  • #3
I was practicing the example from the book and mistakenly used that value haha... Thanks!
 

1. What is charge?

Charge is a fundamental property of matter that describes the amount of electrical force an object possesses. It can be either positive or negative and is measured in Coulombs (C).

2. How are excess electrons created in a rod?

Excess electrons can be created in a rod through various processes such as friction, induction, or contact with other charged objects. These processes transfer electrons to or from the rod, resulting in an excess or deficiency of electrons.

3. What determines the amount of excess electrons in a rod?

The amount of excess electrons in a rod is determined by the material of the rod, the surface area of the rod, and the processes that have occurred to transfer electrons to or from the rod.

4. How does the presence of excess electrons affect the rod?

The presence of excess electrons in a rod creates an electric field around the rod, causing it to be attracted or repelled by other charged objects. This can also result in the rod having a net negative or positive charge.

5. Can excess electrons be removed from a rod?

Yes, excess electrons can be removed from a rod through processes such as grounding or contact with an object with an opposite charge. This will neutralize the rod and disperse the excess electrons.

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