electron Trajectory A Magnetic Field (into the screen) | Trajectory B

A at rest with potentiol difteren ce of proton is 750 V. Atter being field of mognitude accelerated, it enters a mognetic 1T perpendicular ly. a) Find the velocity ot freid atter which the praton enters Hhe mognetic rt accelerated IS b Find the of the proton moving in the orbitol rodlus mapnetic field.

A cyclotron (figure) designed to accelerate protons has an outer radius of 0.333 m. The protons are emitted nearly at rest from a source at the center and are accelerated through 572 V each time they cross the gap between the dees. The dees are between the poles of an electromagnet where the field is 0.720 T. The black, dashed, curved lines Alternating AV represent the path of the particles. -Dg After being accelerated, the particles exit here. -North pole of magnet (a) Find the cyclotron frequency for the protons in this cyclotron. 1.04e33 x rad/s (b) Find the speed at which protons exit the cyclotron. m/s (c) Find their maximum kinetic energy. ev (d) How many revolutions does a proton make in the cyclotron? revolutions (e) For what time interval does the proton accelerate? awranca Barke kay Nationallab

For time varying fields, the electric field is not conservative. Why? Explain withmathematical substantiations.

Use the following constants if necessary. Coulomb constant, k = 8.987 × 10° N · m² /C?Vacuum permitivity, €o = 8.854 x 10-12 F/mMagnetic Permeability of vacuum, o = 12.566370614356 × 10-7 H/m. Magnitude of the Charge of one electron, e = -1.60217662 × 10-19 C. Mass of one electron, me = 9.10938356 x 10¬3' kg. Unless specified otherwise, each symbol carries their usual meaning. For example, µC means micro coulomb . Two long coaxial hollow cylinder of radius a = 2 mmand b = 20 mm with b > a with charge density) = 1 µC/mFind the magnitude of the Electric field at r = 5 mm Magnitude of the Electric field Give your answer up to at least three significance digits. N/C Find the absolute value of the potential difference between the cylinders Potential difference Give your answer up to at least three significance digits. Volts Find the capacitence of the system with length L = 17 m Capacitance Give your answer up to at least three significance digits. F

Q- 2- A sphre P Ruluis R with unifvm chavge p. us Causs Law to Pind the electvic field -

An electron travels from right to left at 3 x 10° m/s when it encounters the B field pictured below. The magnitude of the field is 1Tesla. Draw a picture of the electron's path in the field with the correct direction. Calculate the radius of curvature. х х

=(-1) cos 0 and For what value of A the velocity field in plane polar coordinates given by v, = X Cos e sin 0 satisfies the mass conservation law? OX=rsin 0. A= r cos 0. O None of these. O Any non-zero value of A.

The four is place d at the four line conductor corners ot the sq ure which has long side of a 0.02 m . s A electricity and in figure each with direction as shown Find the nag nng he tie field at poin P (center of }he aquere) Choise 5.07 - 5 10 •P 0.02 67 -4 10 1.13 x -4 c) 1.71 X 1 0 0.02m - 4 2-26 x 10 e) 8. 29 x 10 f)

Given the following arc of current,find the angle of the arc such that theB-field at the center point is 1.26 x10-5 T, the radius 12 cm, and thecurrent 7 A