A uniform magnetic field of magnitude 0.138 T is directed along the positive x a

Question

A uniform magnetic field of magnitude 0.138 T is directed along the positive x axis. A positron moving at a speed of 4.75 times 10^6 m/s enters the field along a direction that makes an angle of theta = 85.0degree with the x axis (see figure below). The motion of the particle is expected to be a helix. Calculate the pitch p of the trajectory as defined in figure. Calculate the radius r of the trajectory as defined in figure. A wire is formed into a circle having a diameter of 20.0 cm and placed in a uniform magnetic field of 3.30 mT. The wire carries a current of 5.00 A. Find the maximum torque on the wire. Find the range of potential energies of the wire-field system for different orientations of the circle.

Explanation / Answer

17) B =0.138 T, v =4.75*10^6 m/s, theta = 85 degrees,

positron mass m= 9.1*10^-31 kg, charge q= 1.6*10^-19 C

F = mv^2/r = qvBsin(theta)

r = mv/qBsin(85)

r = (9.1*10^-31*4.75*10^6)/(1.6*10^-19*0.138*0.996)

r =0.000196 m

(a) pitch p = vx*T = vx*(2pi*r/vx) = 2pi*r

p = 2*3.14*0.000196

p = 0.00123 m

(b) r =0.000196 m

18) d =20 cm , r =10 cm , B =3.3 mT , i =5 A

(a) maximum torque T = MxB = iABsin(90)

T = 5*3.14*0.1*0.1*3.3*0.001*1

T = 520 uJ

(b) U = - M.B

U = -MBcos(0)

Umin = -520 uJ

Maximum potential energy

U = -M.B = -MBcos(180)

Umax = 520 uJ

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