एक बिन्दु ( x , y , z ) पर वैद्युत विभव `V = -x^(2)y –xz^(3) +4` है | इस बिन्दु पर वैद्युत क्षेत्र `vecE` होगा

Options

A. `vecE=hati(2xy+z^(3))+hatjx^(2)+hatk3xz^(2)`
B. `vecE=hati2xy+hatj(x^(2)+y^(2))+hatk(3xz-y^(2))`
C. `vecE=hatiz^(3)+hatjxyz+hatkz^(2)`
D. `vecE=hati(2xy-z^(3))+hatjxy^(2)+hatk3z^(2)x`

Answer

A

Explanation

`E_(x)=-(dV)/(dx)=-[-2xy-z^(3)]`
`E_(y)=-(dV)/(dy)=-[-x^(2)]`
`E_(x)=-(dV)/(dx)=-[-3xz^(2)]`
`therefore vecE=E_(x)hati+E_(y)hatj+E_(z)hatk=(2xy+z^(3))hati+x^(2)hatj+3xz^(2)hatk`.