Question

Q1 Problem 1. 20 Points Problem 1. (20 points) A positive point charge (magnitude 191) with mass m travels to the right at constant speed 7. The charge enters a region with a uniform magnetic field and undergoes uniform circular motion with radius Ri. After the charge leaves the field region, the magnitude of the field is steadily changed over time At (the direction doesn't change). After the field stops changing, a second, identical charge with the same speed is sent into the field region, and undergoes uniform circular motion with a different radius R. (a) (8 points) Determine the direction of the magnetic field in the shaded region, and find the magnetic field magnitudes B; and B, in terms of|g1, m, v and the radii Ri, Ry. Did the magnitude of the field increase or decrease? (b) (8 points) A circular, conducting loop with radius r was entirely in the field region as the field magnitude was changed. The plane of the loop is perpendicular to the magnetic field. Calculate the emf induced in the loop in terms of r, B., B, and At. (e) (4 points) Determine the direction (clockwise or counterclockwise) of the induced current in the loop during the time the magnetic field was changing RE 1 R; Conducting loop

Answer 1

QI: RE Ri conducting loop: laul in Both charged particles lal deflects upwald J directions ie Magnetic foace on the charged pailide is upwardy FM lvi (vxB) But as shown coda di maite axes take the let Ta vi FM = fmj But in →x we know li xG)) =j Hence Magnetic field is ve z direction Magnitic field is (-² +7) Hence is (²) into the plane of paper direction shown in figure above Here intial field - Bi Initial radicy of path = Ri follower Find field = Bf Final radices of path Rf followed But to folloco cucular path Magnette force Centopetal force 'Bloly= mv B- mv Iqlr

For field Bi radius followed Ri → Bi= mv Touri For field Bf radices followed Rf => BF = mv IqIRE from figure since RE Ri & Bath Bi > BF Hence Magnetic field is decreasing. (6) B Br in 7 Y Magnetic field is changed from Bi to a time at Since plane of loop is perpendiculal to B → Magnetic flux 0-BA By Lenz law enf -(T5r2) at -(ory (566) er-do dt d BF-Bi es-dBA dt the ot e = (1r*)( B1-BE at

с to Lenz law, the in According current poroduced in the loop is in such way that it opposes the change extanal Field (8) Since Bifteld is decreasing (Bi+86), the causent induced in clockwise, which tends to increase the external Field loop is B so current induced is ul Clock wise"