Nonconducting Rod electric pot.

In summary, the problem involves a nonconducting rod with a positive linear charge density and an infinite distance away, the electric potential is zero. The goal is to calculate the electric potential at a specific location x=L+d, given the charge density and the distance. The attempt at a solution involves using the equation V=q/4pi epsilon r and integrating to find the electric potential. However, the expression for the distance used in the integration is incorrect and needs to be adjusted for the correct solution to be obtained.
  • #1
Gogeta007
23
0

Homework Statement



There is a nonconducting rod of negligible thickness located along the x axis; its ends have coordinates x = 0 and x = L. It has a positive, nonuniform, linear charge density (lambda) = (alpha)x; alpha is constant. An infinite distance away, th eelectric potential is zero. Show that th electric potential at the location x=L+d is given by:

V= ( alpha/4pi(epsilon0) ) ( (L+d) ln(1+L/d) -L )

Homework Equations



V= q/4pi epsilon r


The Attempt at a Solution



V = integral of dv
dv= dq/4pi(epsilon)r
dq=lambdadx
dq= alpha x dx

dV = ( (alpha) x dx) / (4 pi epsilon (d-x) )

V=constants <integral> xdx/ d-x <===== integration table

<integral> udu/a+bu = 1/b2 (a + bu - a*ln(a + bu) <evaluate from 0 to L>

when I evaluate i get:

(constants) * d-d-L d*ln( d / d - L )

and that's not what I am supposed to get =/



ty
 
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  • #2
Your expression d - x for the distance between your charge element and the location of interest is incorrect. Read the problem. The point of interest is at distance d from the end of the rod at x = L, so any point on the rod must be at distance greater than d from the point of interest. Draw a picture and see for yourself what that distance ought to be.
 

Related to Nonconducting Rod electric pot.

1. What is a nonconducting rod electric pot?

A nonconducting rod electric pot is a cooking pot that is made of a material that does not conduct electricity, such as plastic or ceramic. It is used for cooking or heating food using an electric heat source.

2. How does a nonconducting rod electric pot work?

A nonconducting rod electric pot works by using an electric heating element, typically located at the bottom of the pot, to generate heat. The nonconducting material of the pot prevents the electricity from passing through and instead, the heat is transferred to the food inside the pot.

3. What are the advantages of using a nonconducting rod electric pot?

One of the main advantages of using a nonconducting rod electric pot is its safety. Since the pot is made of a nonconducting material, there is a lower risk of electric shock or fire compared to using a metal pot. Additionally, nonconducting rod electric pots are often lightweight and easy to clean.

4. Can a nonconducting rod electric pot be used on all types of stovetops?

No, a nonconducting rod electric pot is only designed to be used with electric heat sources. It should not be used on gas or induction stovetops as the pot will not heat up properly and may result in damage to the pot or stovetop.

5. Are there any special care instructions for a nonconducting rod electric pot?

Yes, it is important to follow the manufacturer's instructions for cleaning and caring for your nonconducting rod electric pot. Avoid using abrasive cleaners or metal utensils that may scratch the surface of the pot. Additionally, always unplug the pot before cleaning or storing it.

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