For an electric field passing through a flat surface perpendicular to it, the electric flux of the electric field through the surface is the product of the electric field’s strength and the area of the surface. A certain flat surface consists of two adjacent squares, where the side length, in meters, of the larger square is 3 times the side length, in meters, of the smaller square. An electric field with strength 29.00 volts per meter passes uniformly through this surface, which is perpendicular to the electric field. If the total electric flux of the electric field through this surface is 4,640 volts·meters, what is the electric flux, in volts·meters, of the electric field through the larger square?

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Accepted Answer

The correct answer is 4,176. It’s given that the side length of the larger square is 3 times the side length of the smaller square. This means that the area of the larger square is 3 2 , or 9, times the area of the smaller square. If the area of the smaller square is represented by x, then the area of the larger square can be represented by 9x. Therefore, the flat surface of the two adjacent squares has a total area of x + 9x, or 10x. It’s given that an electric field with strength 29.00 volts per meter passes uniformly through this surface and the total electric flux of the electric field through this surface is 4,640 volts·meters. Since it’s given that the electric flux is the product of the electric field’s strength and the area of the surface, the equation 29.00(10x) = 4,640, or 290x = 4,640, can be used to represent this situation. Dividing each side of this equation by 290 yields x = 16. Substituting 16 for x in the expression for the area of the larger square, 9x, yields 9(16), or 144, square meters. Since the area of the larger square is 144 square meters, the electric flux, in volts·meters, of the electric field through the larger square can be determined by multiplying the area of the larger square by the strength of the electric field. Thus, the electric flux is (144 square meters)( 29.00 volts ⁄ meter ), or 4,176 volts·meters.

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