3. A bea m consisting of five types of ions labeled A, B, C, D, and E enters a r

Question

3. A bea m consisting of five types of ions labeled A, B, C, D, and E enters a region that contains a uniform magnetic field as shown in the figure below. The field is perpendicular to the plane of the paper, but its precise direction is not gi table below gives the masses and charges of the ions. Note: 1 mass unit 1.67 x 10 kg a e 1.6x 10-19 C ven. All ions in the beam travel with the same speed. The nd Mass 2 units 4 units 6 units 2 units 4 units Charge te te te Ion Region containing magnetic field Ion beam (a) Which ion falls at position 2? (b) What is the direction of the magnetic field? (c) Determine the magnitude of the magnetic field if ion A travels in a semicircular path of radius 0.50 m at a speed of 5.0 106 m/s.

Explanation / Answer

a)

diameter of the semicircle by each ion is given as

d = 2 m v/(qB)

for A :

dA = 2 mA v/(qA B) = 2 (2 x 1.67 x 10-27) (v/B) /(1.6 x 10-19) = 4.175 x 10-8 m

for B :

dB = 2 mB v/(qB B) = 2 (4 x 1.67 x 10-27) (v/B) /(1.6 x 10-19) = 8.35 x 10-8 m

for C :

dc = 2 mc v/(qc B) = 2 (6 x 1.67 x 10-27) (v/B) /(1.6 x 10-19) = 12.525 x 10-8 m

for D :

dd = 2 md v/(qd B) = 2 (2 x 1.67 x 10-27) (v/B) /(1.6 x 10-19) = 4.175 x 10-8 m

for E :

de = 2 me v/(qe B) = 2 (4 x 1.67 x 10-27) (v/B) /(1.6 x 10-19) = 8.35 x 10-8 m

at position 2 , we have ion B falling.

b)

using right hand rule , the direction of magnetic field comes out to be out of the page direction

c)

radius of the semicircle by ion is given as

r = 2 m v/(qB)

for A :

rA = mA v/(qA B)

0.50 = (2 x 1.67 x 10-27) (5 x 106) /((1.6 x 10-19) B)

B = 0.21 T

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