Question 1 A current-carrying wire is bent into a circular loop of radius R and

Question

Question 1

A current-carrying wire is bent into a circular loop of radius R and lies in an xy plane. A uniform external magnetic field B in the +z direction exists throughout the plane of the loop. The current has the magnitude of I and it is deirected counterclockwise when observing from positive z axis.

What is the magnetic force exerted by the external field on the loop? (Express your Answer in terms of some or all of the variables I, R, and B. )

F= ?

Question 2

A proton moves in a circular orbit 250 mm in radius that is perpendicular to a uniform 0.22-T magnetic field.

a) Determine the proton's angular frequency.

w= ?   

b) Determine the proton's period of motion. (Express your answer with the appropriate units. )

T= ?

c) Determine the proton's speed. (Express your answer with the appropriate units.

v= ?

d) Determine the proton's kinetic energy. (Express your answer with the approprate units.)

K = ?

Explanation / Answer

1) Fnet = 0

2)

a) Apply, m*v^2/r = q*v*B

v/r = q*B/m

w = q*B/m

= 1.6*10^-19*0.22/1.67*10^-27

= 2.1*10^7 rad/s

b) T = 2*pi/w

= 2*pi/2.1*10^7

= 2.99*10^-7 s

c) v = r*w

= 250*10^-3*2.1*10^7

= 5.25*10^6 m/s

d) KE = 0.5*m*v^2

= 0.5*1.67*10^-27*(5.25*10^6)^2

= 2.3*10^-14 J

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