A charge of 4.9 x 10-11 C is to be stored on each plate of a parallel-plate capacitor having an area of 150 mm2 and a plate separation of 3.3 mm. Also, the value of ε0 is 8.85 x 10-12 F/m. (a) What voltage (in V) is required if a material having a dielectric constant of 6.3 is positioned within the plates?

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The scalar triple product computes the magnitude m of the moment of a force vector f about a specified line. it is m = (r × f) · n, where r is the position vector from the line to the point of application of the force and n is a unit vector in the direction of the line. use matlab to compute the magnitude m for the case where f = [12, −5, 4] n, r = [−3, 5, 2] m, and n = [6, 5, −7].

The diagram shows a boulder rolling down a hill into a valley and then up the opposite hill. at which position does the boulder have the greatest kinetic energy? a b c d