Question

In a particular region, the electric potential is given by

V = −αxy⁹z + 2βxy,

where α and β are constants. What is the electric field in this region? (Express your answer in vector form. Use the following as necessary: x, y, z, α, and β.)

Answer 1

a ar we have the relation between electric field (2) and the electric pofential (v) is | #1 ở . > - am - Orka 0 Wher î di h are the whit vektors along d, Y, Z ass nexpectively, 17 nolla Given, V=-axy a2 + a pry - 1 of 1 gry this v=- gany2 +2ßxy a to (-9 aayt + 2 pary) = - gay2 + 2 pry: ou + (- ga suy2 + 2 Buy) gaaz +2 px and, De Paz (-ganyz +2B3y) - 9 any + 0 =- 99 sz. putting these values in ) we have; from (1) E (-9 qy+2py) - (- 90x2 + Year 28») - ( - gaxy) . (gays – 234) î+ (ganz + 2ßn) à + g gryk.