Question

In Griffiths section 4.2.1, we saw that the potential of a polarized object with dipole moment p = Pdt in each element of v

b) Second Transformation V(r) dhe / v. Cear - Area Suco. Pddr (5) This was achieved using this product rule for the divergen

Show the validity of the product rule above using for scalar function f = s-sin(0) and for vector function A = ŝ. (Note that

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Answer #1

ANSWER :

Given that :

Dipole moment :

the electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The electric field strength of the dipole is proportional to the magnitude of dipole moment.

Polarized object p=Pdi (0,0,0) the potential of a polarized object with dipole moment pe part in each element of volume drlislets first calculate y ( 2 ) on 10) - blandit at leasing chean Aule) che Vez-x)+7(4-y)+(2-21)? 2(x-x) (-1) 12 2/(x-x1) 7 (yGradient : 07 - + * î Dreagence : 7,0 = 1 / 3 / (50g) +- auge et 2 X2 where B = Og Št Uoch te Z 7 f = 9 (stsing). = 25 sin o3So, f7 à = ssinax - 3 . f (P. À = -3sing 6 dr -- sind 83 7. (AA). [using ) c) To verity So CEP Ås d z = & A. da for à e kr 2,271 = Jordao dp (psino [ 4ks 48c05a]). The integrand is independent of 430, we use Sd0-277 Saarde = 10fdfocare a stino a 216 48 49 50 4 60 : ke (49) ( 43 ซีก 2 ) - : LRY (21) (2) - - 1 Tk 2 ฯ da da? = SG Åde by using o-

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