what is the solution to these questions? An electric field of intensity 4.1 kN/C

Question

what is the solution to these questions? An electric field of intensity 4.1 kN/C is applied along the x-axis. Calculatethe electric flux through a rectangular plane 0.350 m wide and0.700 m long if the following conditions are true. (a) The plane is parallel to the yz-plane.
Nm2/C
(b) The plane is parallel to the xy-plane.
Nm2/C
(c) The plane contains the y-axis, and its normal makes an angle of50.0° with the x-axis.
Nm2/C
what is the solution to these questions? An electric field of intensity 4.1 kN/C is applied along the x-axis. Calculatethe electric flux through a rectangular plane 0.350 m wide and0.700 m long if the following conditions are true. (a) The plane is parallel to the yz-plane.
Nm2/C
(b) The plane is parallel to the xy-plane.
Nm2/C
(c) The plane contains the y-axis, and its normal makes an angle of50.0° with the x-axis.
Nm2/C
(a) The plane is parallel to the yz-plane.
Nm2/C
(b) The plane is parallel to the xy-plane.
Nm2/C
(c) The plane contains the y-axis, and its normal makes an angle of50.0° with the x-axis.
Nm2/C

Explanation / Answer

      =   E. A    Given      E   =   4.1kN/C      along X axis                         =   4100i^        N/C         (i^is unit vector along X axis)    Area       A   =   0.350* 0.700                         =   0.245   m2    A   =   A* n^    here   A isarea ( in vecor form), n^ is normal unit vector i.e. unit vectornormal to the surface.    a.   for A in YZplane,   n^   =   i^       =>   A   =   0.245i^          yz   =   4100i^ . 0.245 i^                   =     1004.5   kN-m2/C                          (as i^ .i^   =   1)               =>   A   =   0.245k^          yz   =   4100i^ . 0.245 k^                   =   0               (as i^ . k^   =   0)     c.      =   E. A                   =   E* A * cos             given      =   50.00          50.0   =   4100* 0.245 * cos 50.00                      =   0.646   kN-m2/ C                      =   646   N-m2/ C                      =   0.646   kN-m2/ C                      =   646   N-m2/ C

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