Need help on part B jonesci19p26.problem (c19p24) A proton of charge +1.60x 10-1

Question

Need help on part B

jonesci19p26.problem (c19p24) A proton of charge +1.60x 10-19 C and mass 1.67x 10-27 kg is introduced into a region of B 0.118 T with an initial velocity of 1.17x 106 m/s perpendicular to B. What is the radius of the proton's pa? 1.03x1o-1 m You are correct Previous TIs uppose the initial velocity of the proton makes an angle of s0 with the direction of the magnetic field B. What is the pitch of the helix make one compi arcThe pitch is the distance the proton travels along the axis of the helix in the time required for the proton to travels along the axis of the helix in the time required for the proton to loop around the axis. Submit Answer Incorrect. Tries 5/10 Previous Tries

Explanation / Answer

Given,

theta = 50 deg ; v = 1.17 x 10^6 m/s ; B = 0.118 T

the magnetic force on the proton is:

F = q v B sin(theta)

centripital force is:

F = m (v sin(theta))^2/r = q v B sin(theta)

r = mv sin(theta)/Bq

r = 1.67 x 10^-27 x 1.17 x 10^6 x sin50/(0.118 x 1.6 x 10^-19) = 0.079 m

we know that,

v = r w

w = v/r = v sin(theta)/r = 1.17 x 10^6 x sin50/0.079 = 1.13 x 10^7 rad/s

w = 2 pi f = 2 pi/T

T = 2 pi/w = 2 x 3.14/(1.13 x 10^7) = 5.56 x 10^-7 s

So the pitch will be:

v = d/t => d = vt

P = h = v cos(theta) T

P = 1.17 x 10^6 x cos50 x 5.56 x 10^-7 = 0.418 m

Hence, P = 0.418 m

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