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

Explanation

`V(x,y,z)=A(xy+yz+zx) `
` (a) A=[MT^-3I^-1] `
` (b) dv=-Edr. `
` i.e. A(y+z)dx+A(z+x)dy+A(x+y)dz `
` =-E(dxi+dyj+dzk) `
` rArr [A(y+z)i+a(z+x)j+A(x+y)k] `
` [dxxi+dyj+dzk] `
` -E[dxi+dyj+sdzk] `
Equating now, we get,
` E=-A(y+z)i-A(z+x)j-A(x+y)k `
` (c) A=10SIunit, r=(1m,1m,1m) `
` e=-10(2)i-10(2)j_10(2)k `
` =-20i-20j-20k `
Magnitude
` |E|=sqrt(20^2+20^2+20^2) `
` =1200=34.64=35N//C `