Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRev

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Class 12 : Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRev

The document Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRev is a part of the Class 12 Course Physics For JEE.
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Potential due to an Electric Dipole

  • The electric dipole is an arrangement that consists of two equal and opposite charges +q and -q separated by a small distance 2a.
  • Electric dipole moment is represented by a vector p of magnitude 2qa and this vector points in the direction from -q to +q. 
  • To find electric potential due to a dipole consider charge -q is placed at point P and charge +q is placed at point Q as shown below in the figure.
    Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRevA Dipole
  • Since electric potential obeys the superposition principle so potential due to electric dipole as a whole would be sum of potential due to both the charges +q and -q. Thus
    Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRev
    where r1 and r2 respectively are distance of charge +q and -q from point R.
  • Now draw line PC perpandicular to RO and line QD perpandicular to RO as shown in figure. 
  • From triangle POC
    cosθ = OC/OP = OC/a
    therefore OC=acosθ similarly OD=acosθ
    Now ,
    r1 = QR≅RD = OR-OD = r-acosθ
    r2 = PR≅RC = OR+OC = r+acosθ
    Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRev
  • Since magnitude of dipole is |p| = 2qa
    Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRev
  • If we consider the case where r>>a then
    Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRev
    again since pcosθ= p·rˆ where, rˆ is the unit vector along the vector OR then electric potential of dipole is:
    Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRev
    for r>>a
  • From above equation we can see that potential due to electric dipole is inversly proportional to r2 not ad 1/r which is the case for potential due to single charge.
    Potential due to electric dipole does not only depends on r but also depends on angle between position vector r and dipole moment p.

Potential Due To A System Of Charges

  • Consider a system of charges q1, q2,…, qn with position vectors r1, r2,…, r n relative to some origin. The potential V1 at P due to the charge q1 is: 
    Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRevwhere r1P is the distance between q and P
  • Similarly, the potential V2 at P due to q2 and due to q are given by 
    Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRevwhere r2P and r3P are the distances of P from charges qand q3, respectively; and so on for the potential due to other charges.
  • By the superposition principle, the potential V at P due to the total charge configuration is the algebraic sum of the potentials due to the individual charges
    Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRev
  • The electric field outside the shell is as if the entire charge is concentrated at the centre. Thus, the potential outside the shell is given by:
    Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRevwhere q is the total charge on the shell and R its radius. 
  • The electric field inside the shell is zero. This implies that potential is constant inside the shell (as no work is done in moving a charge inside the shell), and, therefore, equals its value at the surface, which is
    Electric Potential of a Dipole and a System of Charges Class 12 Notes | EduRev


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