यदि विद्युत विभव V= 10(xy +yz +xz) है, तो बिन्दु (1, 1, 1) पर विद्युत क्षेत्र की तीव्रता ज्ञात करो।

Explanation

` vecE = - vec (Delta) V`
` vecE = - [(del V)/(del x) hati + (del V)/(del y) hat j + (del V)/( del z) hatk]`
` E_x = (del V)/(d x)`
` E_x = (del)/(del x) [10(xy + yz + xz) ]`
`E_x = 10[ (del)/(del x) (xy) + (del)/(del x) (yz) + (del)/(del x ) (xz) ]`
` E_x= 10 [y + 0 + z ]`
`E_x = 10 [y + z]`
` E_y = (del V)/(del y)`
` E_y = (del)/(del y) [10 (xy + yz + xz ) ]`
` E_y = 10 [(del)/(del y) (xy) + (del)/(dely)(yz) + (del)/(del y) (xz ) ] `
` E_y = 10 [x + z + 0 ]`
` E_y = 10 [x + z]`
इसी तरह ` E_z = 10 [ y+ z ]`
` vecE = E_x hati + E_y hat j + E_z hatk rArr vecE = - [ (del V)/(delx ) hati + (del V)/(del y) hatj + (del V)/(del z) hat k ]`
` vecE = - { 10(y + z)hati + 10 (x + z) hatj + 10 (y + x ) hatk } `
` vecE = -{ 10 (1 +1) hati + 10(1 +1) hatj + 10 (1 +1 ) hatk }`
` vecE = -20 hati - 20 hat j - 20 hatk `