Potential Energy of A Dipole In An External Field

Consider a dipole with charges q₁ = +q and q₂ = –q placed in a uniform electric field E, as shown in Fig. In a uniform electric field, the dipole experiences no net force; but experiences a

Torque =p×E (which will tend to rotate it (unless p is parallel or anti-parallel to E). Suppose an external torque ext is applied in such a manner that it just neutralizes this torque and rotates it in the plane of paper from angle θ₀ to angle θ₁ at an infinitesimal angular speed and without angular acceleration. The amount of work done by the external torque will be given by

This work is stored as the potential energy of the system. A natural choice is to take θ₀ = π / 2. (Αn explanation for it is provided towards the end of discussion.) We can then write,

Here, r₁ and r₂ denote the position vectors of +q and –q. Now, the potential difference between positions r₁ and r₂ equals the work done in bringing a unit positive charge against field from r₂ to r₁. The displacement parallel to the force is 2a cosθ. Thus, [V (r₁)–V (r₂)] = –E × 2a cosθ. We thus obtain,

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Some of these questions which may be asked in your Board Examination 2012-2013

Q1: what are the characteristic of charges acquired by the objects on rubbing against each other?

Q2: Who suggested first that there are two kinds of charges?

Q3: How can you show that there are two types of charges?

Q4: An ebonite rod is rubbed with the fur or wool. What type of charges do they acquire?

Q5: Is mass of body affected on charging?

Q6: What is the polarity of charge?

Answer these questions in comment box and help your friends