Q. 273.7( 27 Votes )

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Answer :

A dipole is a system consisting of two charges equal in magnitude and opposite in nature i.e. a positive charge + q and a negative charge –q separated by some distance d

Electric dipole moment of a dipole is given by,

P = q × d

Where, ‘q’ is magnitude of either of charge (in column)

And ‘d’ is separation between the pair of charges (in metres)

Dipole moment is a vector quantity and its direction is from negative charge to positive charge

We are given dipole moment of the system,

P = 10^{-7}Cm , along negative Z axis

Here Electric Field is varying at the rate of 10^{5} NC^{–1} per metre in positive Z direction

i.e. dE/dl = 10^{5} NC^{–1}m^{-1} along Z direction

so the electric field at any point on z axis at distance of a metres is

Now the total dipole moment equal to 10^{–7} Cm in the negative z-direction.

**The system and the Forces on it are as shown in the figure**

Force on a charged particle in an electric field is given by

F = q × E

Where q is the magnitude of charge and E is the magnitude of Electric Field and the force is same as the direction of electric field in case of a positively charged particle and opposite to the direction of field in case of negatively charged particle

so Force on the + q charge located at a distance l from origin will be

directed towards positive Z axis

(since the electric field on z axis at distance of l metres from origin )

Force on the -q charge located at a distance l + d from origin will be

directed towards negative Z axis

(since the electric field on z axis at distance of l + d metres from origin)

So net force on the system would be

F = F _{+ q} – F_{-q}

(since F _{+ q} is directed towards positive Z axis and F_{-q} is directed towards negative Z axis )

So net force will be

Solving we get

We know,

q × d = P which is the dipole moment of the system so we get

Putting the values of P = 10^{–7} Cm and = 10^{5} NC^{–1}m^{-1} We get

F = - (10^{-7}C × 10^{5}NC^{-1}m^{-1})

i.e. F = -10^{-2} N

Negative sign states that force is along negative Z axis , so the net force on the system is 10^{-2} N in negative Z direction.

We know Torque on an Electric Dipole is Vector or cross product of dipole moment **P** and electric field **E** and is given as

**= P** **E**

which can be further evaluated as

= PE.sin(θ)

is the Torque of the dipole

Where P is the magnitude of dipole moment

E is the magnitude of electric field

is the angle between Dipole moment and electric field

is a unit vector perpendicular to plane containing **P** and **E**

Here dipole moment **P** is along negative z axis and electric field **E** along positive Z axis so angle between them

So, Sin = Sin180 = 0

So whatever be the magnitude of **P** and **E** putting in the equation = PESin

We get the torque **τ** = 0 Nm

So the torque of the system is zero

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