Force on a charge obtained from electric potential

In summary, the electric potential along the x-axis in a certain region of space is given by V = 111x^3 - 517x - 258 where V is in Volts and x is in meters. To find the force (magnitude and direction) experienced by a -444 μC point charge at point (56.5 cm, 0), we use the equations E = dV/dx and F = qE, where E is the electric field and q is the charge. The derivative of 258 with respect to x is 0, so the electric field at (56.5 cm, 0) is -668.7 N/C. However, this answer is incorrect and further analysis is needed.
  • #1
Alan I
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Homework Statement

In a certain region of space, the electric potential along the x-axis is given by:

V = 111x3 - 517x - 258 where V is in Volts and x is in meters.

Find the force F (magnitude in N and direction) felt by a -444 μC point charge at point (56.5 cm,0). (For direction, all you need is the sign.)

Homework Equations


E=dV/dx
F=qE

The Attempt at a Solution


[/B]
dV/dx=d/dx(111x3-517x-258=333x2-517-258=E

⇒ E(0.565m)=-668.7 N/C

⇒F=qE=(-444*10-6)*(-668.7)≅0.297

The answer turned out to be wrong so if someone can give me a hint towards where my mistakes are I would greatly appreciate it!
 
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  • #2
What is the derivative of 258 with respect to x?
 
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Likes Alan I
  • #3
Orodruin said:
What is the derivative of 258 with respect to x?

Thanks!
 

FAQ: Force on a charge obtained from electric potential

What is the relationship between force on a charge and electric potential?

The force on a charge is directly proportional to the gradient of the electric potential. This means that the greater the change in electric potential over a certain distance, the greater the force on the charge will be.

How is force on a charge calculated from electric potential?

The force on a charge can be calculated using the equation F = qE, where q is the charge of the particle and E is the electric field strength. Electric field strength can be determined by dividing the change in electric potential by the distance over which it changes.

What is the difference between electric potential and electric potential energy?

Electric potential is a measure of the potential energy per unit charge at a certain point in an electric field. Electric potential energy, on the other hand, is the energy associated with the position of a charge in an electric field.

How does distance affect the force on a charge from electric potential?

The force on a charge from electric potential decreases as distance from the source of the electric field increases. This is because the electric potential decreases with distance, resulting in a smaller force on the charge.

Can the force on a charge from electric potential be negative?

Yes, the force on a charge from electric potential can be negative. This indicates that the force is acting in the opposite direction of the electric field. This can occur when the charge is moving in the direction of decreasing electric potential.

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