An electric dipole of moment P is placed in a uniform electric field E Drive the expression for the torque experienced by the dipole show diagrammatically the orientation of the dipole in the for which Torque is (i)
maximum (ii) Half the max. value (iii)Zero.
Answers
Answer:
Expression for Torque experienced by a dipole:
The force on charge +q = FA = qE along the direction of vector E
The force on charge –q = FB = qE opposite to the direction of vector E
As these two forces are equal, opposite and parallel so they form a couple
We know that Torque т = Force * Arm of the couple
T = Force X Arm of couple
= F X AB sin Ɵ
= qE X AB sin Ɵ
= qE X 2a sin Ɵ
= (q X 2a) E sin Ɵ
= pE sin Ɵ where p is the dipole moment
= vector p X vector E
Vector form: The expression for torque is vector form is given below:
T = vector p X vector E = pE sin Ɵ
Where p is the dipole moment and E is the uniform Electric field
Case 1: When Ɵ is 900 then Torque is maximum and is equal to pE which means the dipole moment should be perpendicular to the direction of the uniform electric field E.
Case 2: When Ɵ is 00, then Torque is minimum. It is equal to 0 as sin 0 is zero which means the dipole moment should be parallel to the direction of the uniform electric field E.
Case 3: When Ɵ is 300, then Torque is pE/2. It is equal to pE/2 as sin 300 is half which means the dipole moment should be at an angle 300 to the direction of the uniform electric field E.
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Answer:
Show diagrammatically the orientation of the dipole in the field for which torque is maximum , half the maximum value, zero.
Explanation: