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This question is an exercise in manipulating dimensionless quantities. In the following, assume that :3: and 3; have dimensions of length, with the reference length R known, and that q and p have dimensions of charge, with the reference charge Q known. For each expression below (they do not have physical meaning), rearrange the left-hand side and right-hand side into dimensionless quantities. In other words, write everything in terms of 18/ R, y/R: q/Q, and p/Q and then divide/ multiply the equations by factors of R and Q to ensure both sides are dimensionless. For example, 1 l giVen F(s,y) = T obtain RF = 22. "3 +3! (a +e) 1 a) F1(:r.y) : 2, where a is a real number. ' 5": + 2 a. ( :5) b) F2(;I:t y; g) = ( b + b) , where a and b are real numbers. a: y '1 3 4 3 (3) F3 (:17,y,p, q) (3b; ++yb:2]a , where a and b are real numbers. R (1) FAQ}; g) : V/o. :32 j: y2 dm. Hint: consider the change of variable :3" : {It/R