Superposition principle of electric field virtual experiment

Quiz

Q1) A has a charge of +2 µC, and object B has a charge of +6 µC. Which statement is true:

A. $\ F_{AB} $= $\ –3F_{BA}$
B. $\ F_{AB} $=$\ –F_{BA}$
C. $\ 3F_{AB} $=$\ –F_{BA}$

Answer) B.
By Newton’s third law, the two objects will exert forces having equal magnitudes but opposite directions on each other.

Q2) At the position of the dot, the electric field points

A. Up.
B. Down.
C. Left.
D. Right.
E. The electric field is zero.

Answer) A.
The direction of the field is taken to be the direction of the force it would exert on a positive test charge

Superposition principle of electric fields Simulation(Virtual Experiment)

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Force, Charges, and Distance

The electrical force between any two objects obeys a similar inverse-square relationship with distance. The relationship among electrical force, charges, and distance, now known as Coulomb’s law, was discovered by the French physicist Charles Coulomb (1736–1806) in the eighteenth century. Coulomb’s law states that for charged particles or objects that are small compared with the distance between them, the force between the charges varies directly as the product of the charges and inversely as the square of the distance between them.

Coulomb’s law can be expressed as

$\ F = k \frac {q_{A}q_{B}}{d^2}$

where $\ d$ is the distance between the charged particles; $\ q_{A}$ represents the quantity of charge of one particle and $\ q_{B}$the quantity of charge of the other particle; and $\ k$ is the proportionality constant.

When the charges are measured in coulombs, the distance is measured in meters, and the force is measured in newtons, the constant, K, is $\ 9.0 X 10^9 N m^2/C^2$.

This equation gives the magnitude of the force that charge $\ q_{A}$ exerts on $\ q_{B}$ and also the force that $\ q_{B}$ exerts on $\ q_{A}$. These two forces are equal in magnitude but opposite in direction. You can observe this example of Newton’s third law of motion in action when you bring two strips of tape with like charges together. Each exerts forces on the other. If you bring a charged comb near either strip of tape, the strip, with its small mass, moves readily. The acceleration of the comb and you is, of course, much less because of the much greater mass.

The electrical force, like all other forces, is a vector quantity. Force vectors need both a magnitude and a direction. However, Coulomb’s law will furnish only the magnitude of the force. To determine the direction, you need to draw a diagram and interpret charge relations carefully.

Consider the direction of force on a positively charged object called A. If another positively charged object, B, is brought near, the force on A is repulsive. The force, $\ F_{B}$ on A, acts in the direction from B to A, as shown in Figure 1a. If, instead, B is negatively charged, the force on A is attractive and acts in the direction from A to B, as

shown in Figure 1b.

FIGURE 1 The rule for determining direction of force is like charges repel, unlike charges attract.

The superposition principle

• The electric force obeys the superposition principle.

• That means the force two charges exert on a third force is just the vector sum of the forces from the two charges, each treated without regard to the other charge.

• The superposition principle makes it mathematically straightforward to calculate the electric forces exerted by distributions of electric charge.

• The net electric force is the sum of the individual forces.

The Electric Field

The electric field is a vector quantity that relates the force exerted on a test charge to the size of the test charge. How does this work? An electric charge, q, produces an electric field that you can measure. This is shown in Figure 2. First, measure the field at a specific location.

FIGURE 2 Arrows can be used to represent the magnitude and direction of the electric field about an electric charge at various locations.

Call this point A. An electrical field can be observed only because it produces forces on other charges, so you must place a small positive test charge, $\ q′$, at A. Then, measure the force exerted on the test charge, $\ q′$, at this location.

According to Coulomb’s law, the force is proportional to the test charge. If the size of the test charge is doubled, the force is doubled.

Thus, the ratio of force to test charge is independent of the size of the test charge. If you divide the force, F, on the test charge, measured at point A, by the size of the test charge, $\ q′$, you obtain a vector quantity, $\ F/q$′. This quantity does not depend on the test charge, only on the charge q and the location of point A. The electric field at point A, the location of $\ q′$, is represented by the following equation.

Electric Field E

$\ E = \frac {F_{on q'}}{q'}$
$\ E = k\frac {q}{r^2}$.....[single point charge q]

The direction of the electric field is the direction of the force on the positive test charge. The magnitude of the electric field is measured in newtons per coulomb, N/C.

A picture of an electric field can be made by using arrows to represent the field vectors at various locations, as shown in Figure 2.

The length of the arrow will be used to show the strength of the field. The direction of the arrow shows the field direction. To find the field from two charges, the fields from the individual charges are added vectorially. A test charge can be used to map out the field resulting from any collection of charges.

Superposition principle of electric fields

The superposition principle states that, for a collection of charges, the total electric field at a point is simply the summation of the individual fields due to each charge

at any point P, the total electric field due to a group of charges equals the vector sum of the electric fields of the individual charges.