Ascheme for power generation proposes to use conducting balloons that expand and contract in waterfalls (with adequate insulation). consider a balloon of volume v at a given time, with water flowing into it with a flow rate f(m/s). the water falls down into the spherical balloon causing it to expand. the balloon is in a region where the magnetic field is uniform and vertical of magnitude b. a) calculate the proposed induced emf along the equator of the balloon. (horizontal equator), at the moment indicated above. (8 marks) b) indicate the direction of flow of the current around the equator if the field b points down. (2 marks) c) the scheme then allows for the mouth of the balloon to be closed and water to leak out through holes in the bottom when the volume of the balloon becomes 4v. the initial leak rate is 2.5 f. calculate the induced emf along a horizontal ring on the balloon a vertical distance z away from the centre of the balloon. (6 marks) d) calculate the induced emf along the largest vertical circle on the balloon for c)