INTRODUCTION: Hi, here i am stuck with a few problems. One from Magnetism and the rest from Optics. THE PROBLEMS: (1) A wire PQ of mass m can slide frictionlessly on two conducting rails spaced a distance l. A current i flows on into the wire PQ with the help of a current generator.There is a uniform magnetic field B perpenticular to the plane of the frame. (a)If the wire starts its motion with zero initial velocity, find its velocity after t seconds. (b) If instead, the generator is a constant voltage source of emf E and R is the total resistance of the loop, find the final velocity of the wire. WHAT I COULD DO: (1a)The first part is simple.The force on the sliding wire is given by F=Bil. Hence acceleration a=Bil/m and velocity after t seconds is v=at= Bilt/m. WHAT I CANNOT UNDERSTAND: In the first part, i.e. part (a), the sourse is a constant current source. Thats ok. But what is this constant voltage? What is the significance of this constant voltage? Will the velocity be uniform in the second case be uniform? If so, why? And, finally how to go about doing part (b)? THE PROBLEMS (Contd.): (2) (a)A transparent sphere of radius R and refractive index n is kept in air. At what distance from the surface of the sphere should a point object be placed so as to form a real image at the same distance from the sphere? (b) An air bubble is inside water. The refractive index of water is 4/3.At what distance from the air bubble should a point object be placed so as to form a real image at the same distance from the bubble? WHAT MY BOOK SAYS: (a)The answer to the first part is R/(n-1). (b)The answer to the second part is "The air bubble cannot form a real image". WHY I'M FACING A PROBLEM: Although the two questions (a) and (b) look almost the same, but i think there is a slight difference. THE DIFFERENCE I SEE: In both cases the object is kept in the denser medium but in part (a) the refraction takes place at a concave surface whereas in part (b) refraction takes place at the convex surface. That is what i could make out, but still i'm not quite clear about the quesion (a). MY EXACT PROBLEM: Although i could make out some difference but i'm not quite clear about how to go about doing the problems. I'm getting confused again and again. And why can't the air bubble in (b) form a real image? What will happen in that case then? THE PROBLEMS (Contd.): (3) T is a point at the bottom of a tank filled with water, as shown in the diagram. The refractive index of water is 4/3.YPT is the vertical line through T.To an observer at the position O, T will appear to be:(multiple options may be correct) (i)To the left of YT. (ii)Somewhere on YT. (iii)At a depth 3m below T. (iv)At a depth <3m below T. DIAGRAM IN WORDS: In case the diagram is not visible, the point O is directly above the right edge of the tank an the point T is somewhere at the middle of the bottom of the tank. WHAT I KNOW: The position of the apparent image will change with the angle of viewing. So, we can leave out option (ii). I think option (i) has to be correct. WHAT I CANNOT UNDERSTAND: But I'm cant make out what options (iii) and (iv) really want to say. Which of them is correct (if at all)? And why? I really dont understand why an image will be formed "below" T? We are viewing it from a rarer medium and the point T is in water (denser medium). Then why is the term "below T" give in the options (iii) and (iv)? CONCLUSION: I know i shouldn't have posted so many questions all at a time, but any help will be appreciated. Thanks a lot.