An electric field ` ( 2 hai + 3 haj ) N * C ^( - 1 ) ` exists in a region. Calculate the electric flux linked with a square plate of side 0.5 m held parallel to (i) yz - plane and (ii) xy - plane.

Explanation

Electric field , ` vecE = 2 hai + 3 hatj `, so it lies on the xy - plane .
Area of the square plate, ` S = (0.5 ) ^ 2 = 0.25 m ^ 2 `
(i) The vector representation of the plane parallel to the yz - plane is , ` vecS = S hati = 0.25 hati `
` therefore ` Electric flux linked with the square plate
` vec E * vec S = ( 2 hati + 3 hatj ) * ( 0.25 hati ) = 0.5 N * m ^ 2 * C ^ ( - 1 )`
(ii) The vector representation of the plate parallel to the xy - plane is, `vecS = S hatk = 0.25 hak `
` therefore ` Electric flux linked with the sqaure plate
` = vec E * vec S = ( 2 hati + 3 haj ) * ( 0.25 hatk ) = 0 `