In which orientation, a dipole placed in a uniform electricfield is in (i) stable, (ii) unstable equilibrium?

Asked by yadavshekhar962 | 3rd Jan, 2019, 08:38: AM

Expert Answer:

We know, 
Torque tries to align electric dipole in the direction of field. 
 
 
In vector form,
 
tau with rightwards arrow on top equals p with rightwards arrow on top cross times E with rightwards arrow on top
T h u s comma space w h e n
bold italic S bold italic t bold italic a bold italic b bold italic l bold italic e bold space bold italic e bold italic q bold italic u bold italic i bold italic l bold italic i bold italic b bold italic r bold italic i bold italic u bold italic m bold space
stack p space with rightwards arrow on top space i s space a l o n g space E with rightwards arrow on top
theta space equals 0 degree
w h i c h space m e a n s space
tau space equals space p space E space sin 0 degree space equals space 0
H e r e comma space d i p o l e space i s space i n space s t a b l e space e q u i l i b r i u m space w h e n space stack p space with rightwards arrow on top space i s space a l o n g space E with rightwards arrow on top
 
Unstable equilibrium
When dipole is held in direction opposite to E with rightwards arrow on top, torque will turn the dipole through 180° 
 
N e t space f o r c e space i s space minus q E minus q E space equals space minus 2 q E space
tau space equals space p E sin 180 degree space equals negative p E
T h u s comma space d i p o l e space w i l l space b e space i n space u n s t a b l e space s t a t e space

Answered by Shiwani Sawant | 3rd Jan, 2019, 10:31: AM