An ion enters a mass spectrometer which has a 0.18 Tesla field perpendicular to

Question

An ion enters a mass spectrometer which has a 0.18 Tesla field perpendicular to an electric field of 1600 V/m and selects a velocity. The same magnetic field is then used to deflect the singly charged ion into a circular path of radius 12.5 cm. (a) What velocity was selected? (What velocity can pass through the electric and magnetic field without being deflected?) (b) What was the lion mass? A circular loop of wire of cross-sectional area 0.12 m^2 consists of 200 turns, carrying 0.50 A. It is placed in a magnetic field 0.050 T oriented at 30" to the plane of the loop. What torque acts on the loop?

Explanation / Answer

(A) for this Fnet =0

Fnet = Fe - Fm = 0

q E = q v B

E = v B

v = (1600 V/m) / (0.18 T) = 8888.9 m/s

(B) now when only magnetic field is there,

q v B = m v^2 / r

q r B = m v

m = q r B / v = (1.6 x 10^-19) (0.125) (0.18) / (8888.9 )

m = 4.05 x 10^-25 kg ........Ans

--------------------

u = I A = 0.50 x 0.12 = 0.06 A m^2

torque = N( ux B) = N u B sin(theta)

= 200 x 0.06 x 0.050 x sin(90-30)

= 0.52 N m

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