Saved Bookmarks
| 1. |
ln a certain region, the electric potential is given by the formula V (x, y, z) = 2x^(2)y + 3y^(3)z - 4z^(4)x. Find the components of electric field and the vector electric field at point (1, 1, 1) in this field. |
|
Answer» Solution :V(x,y,Z) = `2x^(2) y + 3y^(3)y+3y^(3)z -4z^(4)x` `:. E_(x)=- (delV)/(delx)` `=- (del)/(delx)(2x^(2)y + 3y^(3)z - 4z^(4)x)` `:. E_(x) = -(4xy+0-4z^(4))` Putting x =1 , y =1 , z=1 `E_(x) = -(4-4) ` `E_(x) = 0` and `E_(y) =-(delV)/(dely)` `=- (del)/(dely) ( 2x^(2)y+3y^(3) z-4z^(4)x)` `:. E_(y) =- (2x^(2)+9y^(2)z-0)` `:. E_(y) = -(2x^(2)+9y^(2)z)` Putting x =1 , y =1 , z=1 `:. E_(y) = -(2+9) =-11 ` and `E_(z) =-(del)/(delz) (2x^(2)y+2y^(3) z-4z^(4)x)` `= - (0+3y^(3)-16z^(3)x)` Putting x =1 , y=1 , z=1 `E_(z) = (0+3-16) =13` Putting the value of COMPONENTS in equation `vecE=Exhati+Eyhatj+Ezhatk` `=0hati-11hatj-13hatk` `= - 11hatj +13hatk` |
|