Question

The torque experienced by a dipole is maximum when angle between p and e is

Answer 1

Answer:

So Torque is maximum on Dipole if angle between P amd E is 90 degree...

Answer 2

Answer:

As we know that Torque is that physical quantity Which Rotates the body When it acts on it...Torque is a vector Quantity and it is acts between the Two quantities which are acting at the Right angle (Normal) to each Other...

Torque can be calculated by the Cross Product of Two vector ( We use Cross product only for those vectors which are acting Normal to each other ) and the Direction of the troque can be determined by Right Hand Curl rule which is normal to the Plane formed by these two Vectors...

For example : If A and B are two vectors and they are acting perpendicular to each Other..then Their cross product Represent as T = A X B ( This is a vector Notation of torque )

T = ABsin@ n where

ABsin@ = Magnitude of the torque

@ = Angle between the vector A and B

n = unit vector normal to the plane...

Similarly When an Electric Dipole placed in an Electric Field , It experiences a torque because of which it starts Rotating...Here We have two vectors One is P = Dipole Moment and other vector is E = Electric Field..

P = Dipole Moment is actually efectiveness of a Dipole Which responses differently when placed in Different magnitude of E ( Electric Field ). This is a measurable quantity and can be calculated by the Product of 2r x q i.e,

P = (2r) x q where 2r = Distance between the charges forming Dipole, q = Magnitude of the Charge...P is a vector quantity as its dirwction is from Negative to Positive Charge...

E = Electric field is that physical quantity which applies force when a charge particle enters in that E...Due to this Charge particle accelerates along the direction of E...The Source of E is a Charge as per the relation

E = k Q / r^2 where k is the coloumb constant...Bere you can see E is directly depends on Charge Q..if there is no Charge i.e, Q =0 then E = 0...So source of E is charge...E is a vector quantity its direction depends on the Charge whether it is Negative or Positive...

When Dipole of electric moment P is Intriduced in an Electric Field E...then it Experience a Torque T (tau a greek letter)..

then T = P X E ( Vector Form )

T = PESin@( Magnitude Only)

Here @ is the angle between P and E...Once Dipile is formed its P is fixed and E is also fixed...(Note these quantites will not remain constant always they may vary also depending on situtaion)

Here we consider P and E as constant...So Torque Depends only on the angle between P and E i.e @

Now we know that Sin@ is maximum only if Sin@ = 1

Sin@ = Sin90 => @ = 90 ( Sin@ have maximum value 1 and minimum value -1...See the graph of Sin..you will fimd Sin graph oscillate between 1 and -1...whoch means The maximum value is 1 and the min value is -1...

Thus Torque is Maximum only if the angle between the P and E is Maximum i.e, Sin@ has to be Maximum...and Sin@ is maximum only if @ = 90 degree...

So Torque is maximum on Dipole if angle between P amd E is 90 degree....Hope this help...