Each of the surfaces listed below is a flat plate with area vector that lies in

Question

Each of the surfaces listed below is a flat plate with area vector that lies in a region of uniform electric field . Rank the surfaces in order of the electric flux through them, from most positive to most negative.

Surface 1: A = (5 m^2)i - (4m^2)j    E = (3 N/C)i + (4 N/C)j Surface 2: A = (5 m^2)i - (4m^2)j    E = (3 N/C)i - (4 N/C)j Surface 3: A = (5 m^2)i    E = (3 N/C)j + (4 N/C)k Surface 4: A = (5 m^2)i - (4m^2)j    E = (3 N/C)j - (4 N/C)k Surface 5: A = (5 m^2)i    E = (3 N/C)i + (4 N/C)j Thanks for any help!!! Surface 1: A = (5 m^2)i - (4m^2)j    E = (3 N/C)i + (4 N/C)j Surface 2: A = (5 m^2)i - (4m^2)j    E = (3 N/C)i - (4 N/C)j Surface 3: A = (5 m^2)i    E = (3 N/C)j + (4 N/C)k Surface 4: A = (5 m^2)i - (4m^2)j    E = (3 N/C)j - (4 N/C)k Surface 5: A = (5 m^2)i    E = (3 N/C)i + (4 N/C)j Thanks for any help!!!

Explanation / Answer

Flux f = E.A Surface 1: Flux f1 = (3 N/C)i + (4 N/C)j . (5 m^2)i - (4m^2)j               = 15 - 16               = -1 Nm^2/C (RANK 4) Surface 2 : Flux f2 = (3 N/C)i - (4 N/C)j . (5 m^2)i - (4m^2)j              = 15 + 16              = 31 Nm^2/C   (RANK 1) Surface 3: Flux f3 =  (3 N/C)j + (4 N/C)k . (5 m^2)i                 = 0   (RANK 3) Surface 4:   Flux f4 = (3 N/C)j - (4 N/C)k . (5 m^2)i - (4m^2)j                = - 12 Nm^2/C (RANK 5) Surface 5: Flux f5 = (3 N/C)i + (4 N/C)j . (5 m^2)i              = 15  Nm^2/C   (RANK 2)   RANK 1   : surface 2                            = 15 + 16              = 31 Nm^2/C   (RANK 1) Surface 3: Flux f3 =  (3 N/C)j + (4 N/C)k . (5 m^2)i                 = 0   (RANK 3) Surface 4:   Flux f4 = (3 N/C)j - (4 N/C)k . (5 m^2)i - (4m^2)j                = - 12 Nm^2/C (RANK 5) Surface 5: Flux f5 = (3 N/C)i + (4 N/C)j . (5 m^2)i              = 15  Nm^2/C   (RANK 2)   RANK 1   : surface 2                               = 0   (RANK 3) Surface 4:   Flux f4 = (3 N/C)j - (4 N/C)k . (5 m^2)i - (4m^2)j                = - 12 Nm^2/C (RANK 5) Surface 5: Flux f5 = (3 N/C)i + (4 N/C)j . (5 m^2)i              = 15  Nm^2/C   (RANK 2)   RANK 1   : surface 2                              = - 12 Nm^2/C (RANK 5) Surface 5: Flux f5 = (3 N/C)i + (4 N/C)j . (5 m^2)i              = 15  Nm^2/C   (RANK 2)   RANK 1   : surface 2                 RANK 2   : surface 5 RANK 3   : surface 3 RANK 4   : surface 1 RANK 5   : surface 4               

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