Question

An electric field having an intensity of 275 N/C runs directly along the x-axis of a
coordinate system. A thin rectangular sheet having a length of 1.00 m and a height
of 0.500 m is oriented in various ways to investigate the electric flux. Find the electric
flux when: (a) the sheet is parallel to the plane formed by the y and z axes (i.e., the
normal to the plane is in the direction of the x axis); (b) the sheet is parallel to the
plane formed by the x and y axes; and (c) the normal to the sheet makes a 30◦ angle
relative to the x axis.

Answer 1

Answer on Question #65024-Physics-Other

An electric field having an intensity of $275\,\mathrm{N}/\mathrm{C}$ runs directly along the x-axis of a coordinate system. A thin rectangular sheet having a length of $1.00\,\mathrm{m}$ and a height of $0.500\,\mathrm{m}$ is oriented in various ways to investigate the electric flux. Find the electric flux when: (a) the sheet is parallel to the plane formed by the y and z axes (i.e., the normal to the plane is in the direction of the x axis); (b) the sheet is parallel to the plane formed by the x and y axes; and (c) the normal to the sheet makes a $30{}^{\circ}$ angle relative to the x axis.

Solution

(a)

$$\Phi = E A \cos \theta = E A \cos 0{}^{\circ} = E A = E l h = 275(1)(0.5) = 137.5\,\frac{N m^{2}}{C}.$$

(b)

$$\Phi = E A \cos \theta = E A \cos 90{}^{\circ} = 0.$$

(c)

$$\Phi = E A \cos \theta = E A \cos 30{}^{\circ} = E l h \cos 30{}^{\circ} = 275(1)(0.5) \cos 30{}^{\circ} = 119\,\frac{N m^{2}}{C}.$$

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