A perfectly conducting metal plate is placed in x-y plane

A perfectly conducting metal plate is placed in x-y plane in a right handed coordinate system. A charge of +32πε₀ √2 coulombs is placed at coordinate (0, 0, 2). ∈₀ is the permittivity of free space. Assume î , ĵ , k̂ to be unit vectors along x, y and z axes r espect i vely. At t he coor di nat e. (√2, √2,0), the electric field vector ^{^→}E (Newtons/ Coulomb) will be

E = E₁ + E₂ =	1			Q₁R₁	+	Q₂R₂
	4πε₀			R₁³		R₂³

E =	1			Q₁	( √2a_x + √2a_y - 2a_z ) -	Q₁	( √2a_x + √2a_y + 2a_z )
	4πε₀			16√2		16√2

=	Q	[-4a_z ] =	32√2 πε₀	(-a_z)
	16√2 × 4πε₀		16√2 πε₀

E = -2a_z