The uniform 27.0 mT magnetic field in the figure points in the positive z -direc

Question

The uniform 27.0 mT magnetic field in the figure points in the positive z-direction. An electron enters the region of magnetic field with a speed of 4.60 ×106m/s and at an angle of 30? above the xy-plane. (Figure 1)

Part A

Find the radius r of the electron's spiral trajectory.

Express your answer with the appropriate units.

Part B

Find the pitch p of the electron's spiral trajectory.

Express your answer with the appropriate units.

1 of 1

The uniform 27.0 mT magnetic field in the figure points in the positive z-direction. An electron enters the region of magnetic field with a speed of 4.60 ×106m/s and at an angle of 30? above the xy-plane. (Figure 1)

Part A

Find the radius r of the electron's spiral trajectory.

Express your answer with the appropriate units.

Part B

Find the pitch p of the electron's spiral trajectory.

Express your answer with the appropriate units.

1 of 1

Explanation / Answer

Given,

B = 27 mT ; v = 4.6 x 10^6 m/s ; theta = 30 deg

A)vx = 4.6 x 10^6 cos30 = 3.98 x 10^6 m/s

We know that the magnetic and centripital force balances

m v^2/R = q v B

R = mv/Bq

R = 9.1 x 10^-31 x 3.98 x 10^6/(27 x 10^-3 x 1.6 x 10^-19) = 8.38 x 10^-4m

Hence, R = 8.38 x 10^-4 m

B)Time taken

T = 2 pi m/B q

T = 2 x 3.14 x 9.1 x 10^-31/(27 x 10^-3 x 1.6 x 10^-19) = 1.32 x 10^-9 s

Pitch = P = vy T

P = 4.6 x 10^6 x sin60 x 1.32 x 10^-9 = 3.04 x 10^-3 m

Hence, P = 3.04 x 10^-3 m = 3.04 mm

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