The electric potential existing in space is `V(x,y,z)=A(xy+yz+zx)`
(a) Write the dimensional formula of A.
(b) Find the expression for the electric field.
(c) If A is 10 SI units, find the magnitude of the electric field at `(1 m, 1 m, 1 m)`

Answer

B, C

Explanation

a. `[A]=([V])/([xy])=([ML^2T^-3A^-1])/([L][L])`
`=[ML^-3A^-1]`
b. `E=-[(delV)/(delx)hati+(delV)/(dely)hatj+(delV)/(delz)hatk]`
c. Sunstituting `A=10, ximplies1, y=1` and `z=1` in the expression of part b we have
`E=(-20hati-=20hatj-20hatk)N//C`
`:.|E|=sqrt((-20)^2+(-20)^2+(-20)^2)`
`=20sqrt3N//C`