Electric Field at a Point on the x-Axis Due to Charges

In summary, the potential at a point x on the x-axis due to some charges is given by V(x) = 20/(x^2-4) V. The electric field E at x=4µm is -40x/(x^2-4)^2 V/µm. This is obtained by using the quotient rule to differentiate V(x) and then plugging in x=4.
  • #1
gracy
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Homework Statement


The potential at a point x(measured in µm)due to some charges situated on the x-axis is given by ##V(x)##=##\frac{20}{x^2-4}##V.The electric field ##E## at x=4µm is ?

Homework Equations


##E##=-##\frac{∂V}{∂r}##

The Attempt at a Solution


Actually I have solution but still I am unable to understand.So ,instead of my attempt at a solution .I 'll post solution itself.
##Ex##=-##\frac{∂V}{∂x}## (1)

= -##\frac{d}{dx}(\frac{20}{x^2-4})## (2)

=##\frac{40x}{(x^2-4)^2}## (3)

##Ex## at x=4µm =##\frac{10}{9}##V/µm
Here I am not able to understand how it proceeded from (2) to (3)
 
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  • #3
And how to proceed from (3) to answer?
 
  • #4
You just plug in x=4 into the expression, right?
 
  • Like
Likes gracy
  • #5
blue_leaf77 said:
right?
Yes,of course.
 

Related to Electric Field at a Point on the x-Axis Due to Charges

1. What is an electric field problem?

An electric field problem is a situation in which there is a disturbance or imbalance in the distribution of electric charges, resulting in an electric field that can affect the motion of other charged particles or objects.

2. How do you calculate the electric field in a given problem?

The electric field is calculated using the formula E = kq/r^2, where E is the electric field strength, k is the Coulomb's constant, q is the magnitude of the charge, and r is the distance between the charge and the point where the field is being measured.

3. What factors can affect the strength of an electric field?

The strength of an electric field can be affected by the distance between charges, the magnitude of the charges, and the medium in which the charges are located. The presence of conductors or insulators can also impact the strength of an electric field.

4. How is an electric field problem solved?

To solve an electric field problem, it is important to identify the known and unknown variables, and then use the appropriate formulas and principles of electrostatics to calculate the desired quantities. This may involve using vector addition or integration, depending on the complexity of the problem.

5. What are some real-life applications of electric field problems?

Electric field problems have a wide range of applications in technology, such as in the design of electronic circuits and devices, as well as in understanding natural phenomena such as lightning strikes and the behavior of charged particles in the atmosphere. They also play a crucial role in medical imaging techniques such as MRI scanners.

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