Direction of electric field from positive to negative Direction of electric field from positive to negative ?

Chapter-1

Electric Field Line

The idea of Lines of force was given by Michel Faraday. The imaginary lines which give visual idea of Electric field, its magnitude and direction called electric field line.The electric field line has following property.

Start and Terminate: The electric field line start from Positive charge and terminate at negative charge. The electric field line do not make continuous loop.
Direction of electric Field Line:Direction of electric field is given by the tangent of electric field line at that point.
Relative Strength of Electric Field: Concentration (density) of electric field lines shows the relative strength of electric field at a point. It will give only general idea about electric field not exact value.
Electric Field line Never Cross Each Other:Two lines do not cross each other because if they cross, then at the point of intersection there would be two direction of force which is not possible. Therefore the intersection of two electric field line not possible.
Starting and Terminating Angle of Electric Field Line:If electric field is not perpendicular then it will make an angle with the surface then force F=qE can be resolve as qEalong the surface. This net force should move the charge. But we find charge not moving. So the component of acting force qE should be zero. And the charge and electric field is not zero so should be zero. The will zero for =. Hence we can say that electric field line always right angle to surface.
Explaining Attraction: An electric field line behave stretched string which is always trying to reduce its length.This explains the existence of the electric force of attraction between two oppositely charged objects.
Electric field line repel each other: The electric field lines repel transversally.Due to this,they tend to separate from each other in the direction perpendicular to their lengths. This explains the electric force of repulsion between like charges.
Shape for pair of charges:Shape due to pair charge shown in below figure, in the case of same nature of charge the electric field at the mid of the charges is zero because there is no electric field line. But in the case of opposite nature of charge the electric field at mid is maximum.

Figure: Field line of same nature of Charge

Figure: Field line of opposite nature of Charge

Electric Dipole

If two equal and opposite charges are separated by a small distance, the system is said to form a dipole. The most familiar example is H₂0 .The product of the magnitude of charge and separation between the charges is called dipole moment p. The mid-point of locations of –q and q is called the Centre of the dipole. As below shows charges +q and – q separated by a small distance. Then according to definition dipole moment.

……………………………….(1)

Figure: Electric dipole

The dipole moment is a vector quantity. Eqn. (1) gives its magnitude and its direction is from negative charge to positive charge along the line joining the two charges (axis of the dipole). Having defined a dipole and dipole moment, we are now in a position to calculate the electric field due to a dipole. The electric field of the pair of charges (–q and q) or dipole at any point in space can be found out from Coulomb’s law and the superposition principle.The calculations are particularly simple in the following cases.

CASE I:Electric Field Due To Dipole At An Axial Point: End – On Position

To drive an expression for the electric field of a dipole at a point P which lies on the axis of dipole as shown in figure. This is known as end on position. The point charges –q and +q at point A and B separated by a distance 2l. The point O is middle of the AB. Assume that point P is at a distance r from the mid point O. The electric field at point P due to +q at B is given by Coulumb’s law

Figure : Electric Field Due to Dipole at an Axial Point

In the direction of AP …………………(1)

Similarly electric field at point P due charge –q is

In the direction of PA …………………(2)

Resultant field E in the direction of because is greater than as [ ( is less than ()]

………………………………………………… (3)

Where dipole moment and , also we can write above equation as

If >>> then will be very small compare to 1. So it can be neglected and the expression of the electric field then simplified to

………………………………………………………………(4)

Or ……………………………………………………………(5)

It shows that electric field is in the direction of p and its magnitude is inversely proportional to the third power of distance of the observation point from the centre of the dipole.

CASE II: Electric field due to a dipole at a point on the perpendicular bisector: Broad-on position

Suppose that point P lies on the perpendicular bisector of the line joining the charges shown in below Fig. Assume that AB=, and

Figure: Electric field due to a dipole at a point on the perpendicular bisector

The angle is shown in above Fig. From right angledPAO and PBO it can be written that

The field at P due to charge + q at B in the direction of BP can be written as

Similarly, the field at P due to charge at A in the direction of PA is given as

Note that the magnitudes of, and, are equal.

Let us resolve the fields and parallel and perpendicular to AB. The component perpendicular to AB have opposite in direction so they will cancel out each other. But the components parallel to AB both point in the same direction. Hence, the magnitude of resultant electric field at P is given by

But , Using this expression in the above result, the electric field at P is given by

But p = 2lq. If , the factor can be neglected in comparison to unity. Hence

……………………………………………..(6)

Note that electric field due to a dipole at a point in broad-on position is inversely proportional to the third power of the perpendicular distancebetween P and the line joining the charges.

If we compare Eqns. (5) and (6), we note that the electric field in both cases is proportional to 1/. But there are differences in details:

The magnitude of electric field in end-on-position is twice the field in the broad-on position.

The direction of the field in the end-on position is along the direction of dipole moment, whereas in the broad-on position, they are oppositely directed.

Electric Dipole in a Uniform Field : A uniform electric field has constant magnitude and fixed direction. Such a field is produced between the plates of a charged parallel plate capacitor. Pictorially, it is represented by equidistant parallel lines. Let us now examine the behavior of an electric dipole when it is placed in a uniform electric field.

Let us choose x-axis such that the electric field points along it. Suppose that the dipole axis makes an angle 0 with the field direction. A force qЕ acts on charge +qalong the +x direction and equal force acts on the –q in the –x direction. Two equal, unlike and parallel forces form a couple and tend to rotate the dipole inclockwise direction. This couple tends to align the dipole in the direction of external electric field E. The magnitude of torque is given by

Figure:Electric Dipole in a Uniform Field

In vector form, we can express this result to

We note that when, the torque is zero, and for = 90°, the torque on the dipole is maximum, equal to pE. So we may conclude that the electric field ten s to rotate the dipole and align it along its own direction

Physical significance of dipoles

The centres of positive charges and of negative charges lie at the same place in most of molecules. So their dipole moment is zero. CO₂ and CH₄ are of this type of molecules. However, they develop a dipole moment when an electric field is applied. But in some molecules, the centres of negative charges and of positive charges do not coincide. Therefore they have a permanent electric dipole moment, even in the absence of an electric field. Such molecules are called polar molecules. Water molecules, H₂O, is an example of this type. Various materials give rise to interesting properties and important applications in the presence or absence of electric field.