Electric Charges and Fields Test 10

Though water and ammonia are covalent molecules, they have a net dipole moment due to their distorted structure than the ideal one. Hydrochloric acid has a linear molecular structure but its net dipole moment is towards the Hydrogen atom. But methane has a symmetrical tetrahedral structure and its net dipole moment is zero hence it doesn’t behave as a permanent dipole. Methane solvents are therefore non-polar solvents.

The dipole moment is defined as the product of a charge and distance. The dimension of charge (current*time) is [I T] and the dimension of distance is [L]. Therefore the dimension of dipole moment is [L T I]. Its unit in the CGS and the SI system are esu*cm and C*m respectively.

Dipole is defined as two equal but opposite charges, kept at a small distance and having a dipole moment. The dipole moment is simply the product of the electric charge and length of the dipole. The dielectric constant of the medium doesn’t affect the dipole moment i.e. dipole moment of an electric dipole will be the same in water as well as in the air.

An electric dipole consists of two point charges. The amount of charges is the same but their polarities are different. Therefore the sum of total charges in a dipole is always 0. But flux from a closed surface is related to the total charge inside a surface. As the total charge inside the cube is zero, so there will be no flux coming out or going in towards the surface.

Dipole is the combination of two equal but opposite charges, kept at a certain distance. If it is placed in a uniform electric field, both the charges will suffer the same but opposite forces on them. As a result, the net force on the dipole becomes zero, but due to equal and opposite forces acting on two different points, there is a net torque acting on the dipole.

In the case of a non-uniform electric field, the force acting on both the charges of the dipole will be unequal. So, there will be a net force acting on the dipole in a certain direction. Also, there will be a torque due to two forces acting at two different points. But in case of a uniform electric field, the net force on the dipole will be zero but net torque will be non-zero.

Torque acting on a dipole is p*E*sinθ where E is the electric field. Now θ is 0 degree, so sinθ becomes 0 and hence no torque acts on the dipole. So in this case, no force or torque acts on the dipole. Therefore it will be the condition of stable equilibrium. In the case of θ=180 degree, sinθ is also 0 but the condition is known as unstable equilibrium i.e. if we rotate the dipole a bit, it will not come back to its initial position.

A non-polar substance consists of a huge number of dipoles in it, but they are oriented randomly and hence the net dipole moment of the substance becomes 0 and it acts as a non-polar substance. But if it is placed in an electric field, the dipoles present in it will orient themselves in the direction of the field and hence a net dipole moment will be observed, known as induced dipole moment. No current flow or oscillation of the substance will be observed.

Dipole moment of the dipole = 1*10^-6*5*10^-2 C. m=5*10^-8 C. m. Given the electric field-intensity is E=3*10⁵ N/C. Therefore required torque will be p*E*sinθ where θ is the angle between the electric field and the dipole moment = 90 degrees. Therefore torque required in this case will be 5 *10^-8*3*10⁵*sin 90 N. m=15*10^-3 N. m.

If the distance of a point charge, kept on the axis of a dipole, is sufficiently large than the separation between the charges of a dipole, then it can be shown that electric field E at a distance r from the dipole varies as E α 1/r³. Now if the distance becomes 2r, electric field intensity will decrease by a factor of 2³=8 times. Therefore the force F will now become F/8.