# Electric fields and equipotentials

• dasblack
In summary, The force on the test charge in Newtons is 190 to the right, and the electric field in Newtons/coulomb is -4.75e7. The work done in joules in moving a charge of 2.5μC a distance of 22 cm along an equipotential at 9~V is -2.25e-5 J.
dasblack

## Homework Statement

The figure below shows a test charge q between the two positive charges. Find the force (in Newtons) on the test charge for q = -4 µC.
a)Give a positive answer if the force is to the right and a negative answer if the force is to the left.

b.)For the previous question, find the electric field (in Newtons/coulomb) at the position of test charge. Again, supply a positive value if the electric field points to the right and a negative value if it points to the left.

F=ke|q1|q2|/r^2
E=F/qo

## The Attempt at a Solution

a)F21=ke(2x10-6)(4x10-6)/(3x10-2)^2 = 80 to the left
F23=ke(4x10-6)(3x10-6)/(2x10-2)^2 = 269.7 to the right
F2 = 190

b)E=190/-4x10-6 = -4.75e7

## Homework Statement

How much work (in joules) is done in moving a charge of 2.5μC a distance of 22 cm along an equipotential at 9~V?

## Homework Equations

W=-change in PE, where PE = q(change in volts)

## The Attempt at a Solution

W=-2.5e-6(9)= -2.25e-5 J

Hmm I'm not sure about the negative for qo

I would like to provide some additional information and clarification about electric fields and equipotentials.

Electric fields are created by electric charges and can be described as the force per unit charge at a given point in space. They are represented by vector arrows that indicate the direction of the force on a positive test charge at that point. The strength of the electric field is determined by the magnitude of the charges and the distance between them.

Equipotentials, on the other hand, are imaginary lines that connect points in space that have the same electric potential. Electric potential is a scalar quantity that represents the amount of work needed to move a unit charge from one point to another. Equipotentials are perpendicular to electric field lines and indicate that no work is done in moving a charge along them.

In the first problem, the force on the test charge can be calculated using Coulomb's law, which states that the force between two charged particles is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them. The electric field at the position of the test charge can then be found by dividing the force by the test charge.

In the second problem, the work done in moving a charge along an equipotential can be found by multiplying the charge by the change in electric potential. This is because electric potential is defined as the amount of work needed to move a unit charge between two points.

I hope this additional information helps to clarify the concepts of electric fields and equipotentials.

## 1. What is an electric field?

An electric field is a physical field that is created by electrically charged objects and is responsible for the attraction and repulsion of those charges. It is represented by lines of force that show the direction and strength of the field.

## 2. How are electric fields and equipotentials related?

Electric fields and equipotentials are closely related because equipotential lines are always perpendicular to electric field lines. This means that the potential difference between any two points along an equipotential line is zero, and the electric field is always pointing in the direction of decreasing potential.

## 3. What is an equipotential surface?

An equipotential surface is a surface in an electric field where the potential at every point on the surface is the same. This means that no work is required to move a charge within an equipotential surface, as the potential difference is zero.

## 4. How are electric fields and equipotentials used in practical applications?

Electric fields and equipotentials have many practical applications, such as in electronic devices, capacitors, and electric motors. They are also used in medical imaging techniques like electrocardiograms (ECGs) and electroencephalograms (EEGs).

## 5. How can I determine the strength and direction of an electric field?

The strength and direction of an electric field can be determined by using Coulomb's Law, which states that the magnitude of the electric field at a point is directly proportional to the magnitude of the charge creating the field and inversely proportional to the square of the distance from the charge. The direction of the electric field is given by the direction of the force on a positive test charge placed in the field.

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