Please write in clear hand writing.

Answer each question in one or two complete sentences, mathematical expressions and diagrams as necessary. Make certain you explain your logic. Answers without clear work receive no credit. 1 - = k = 9 x 109 Nm2 AV = E; ATTEO C2 ; E = k 2; F = qE;V = k-; Art Po + 1 x 10-7_ 7; dB = Ho qu xr 4 TT 471 73 ; dB = Holdl x r -; B = Ho i 47 23 ;M = IA e = 1.6 x 10-19C; me = 9.11 x 10-31kg ; mp = 1.67 x 10-27kg 4. (15) A piece of wire is bent into a loop with two concentric arcs as shown below. The inner arc has a radius of R. The outer arc has a radius of 3R. There is a current I introduced into the loop. A) What is the direction of the magnetic field at the dot shown on the diagram? B) Which pieces of the loop contribute to the magnetic field at the point of interest? Explain. C) Write an integral expression to determine the magnetic field at the dot (center of curvature of both arcs). 5. (10)A bar magnet is hung by a string tied to its center so that it is horizontal. It orients so that the north pole of the bar magnet is pointing north (i.e. it acts as a compass). You charge a plastic rod such that it develops a positive charge. You bring this near the south pole of the magnet and it attracts the magnet. You are going to bring it near the north pole of the magnet, what will happen and why?Answer 4 . (A ) According to right hand thumb rule , the direction of magnetic field is negative z- axis , when the current is flowing in the clockwise direction and positive 2 - axis when current plows in anti clockwise direction . ( B ) I clockwise antilack X wise R BR - The curved pieces of loop : ( is one with radius R ( ii) One with radius 3 R . - Both the pieces will contribute to the magnetic field at origin ( the point of interest ) . - magnetic field at the centre due to circular coil ; B B = MOI 2. x where r= radius of circular coil . of the coil is quater (1/4 ) of the loop ( as shown in this problem ) , then magnetic fifd , B : B = 4 ( - MOImagnetic field due to coil of radius R , By ! B , = L M. I ( 2 ) S+2 : Because current E is in Anticlockwise magnetic field due to coil of radius 3 R , B2: MOI ) ( - 2 ) B2 = 4 ( 2.3 R S. 72 : Because current is clockwise Total Magnetic field at origin , Biotal Btotal = B, + Bg = = ) [ + 3] (2) 8 ( Mo Z ) 2 Total field at origin is , Mo I 6 in positive 2- axis 2R Answer of part ( A ) as well . ( c) Integral expression for both the coils of radius R and 3 R respectively to determine magnetic field at origin; of B. de = M. Ienclosed Ampere's circuital Lawe . ie . Line . Integral of magnetic field over the closed boop is to times the current enclosed.Answer 5. magnetic field limes N+ going from North to south of a bar magnet. The direction of magnetic field lines in a ban magnet is from North to South because North pole is considered to be positively charged and South pole to be negative . - The phenomenon observed in the problem is because , when the positively charged plastic ood is brought near the south pole, it attracts the magnet as south pole is negatively charged similarly , when plastic rod is brought near the North pole of a bar magnet , it repels the magnet as North pole is positively charged and alike charges repels each other