An ion with a charge of -4e and a mass of 1.34 x 10^-26 kg is accelerated by a p

Question

An ion with a charge of -4e and a mass of 1.34 x 10^-26 kg is accelerated by a potential of 350V. The ion enters a magnetic field and is pulled into a circular path of radius 45.0cm. What is the strength of the magnetic field? A 400 turn circular coil with a radius of 15.0cm is placed in a magnetic field of 0.500T ( directed perpendicular to the face of the coil ). What is the magnitude of the induced EMF when the magnetic field is changed to 0.300T ( in the opposite direction) in a time of 0.25 seconds ?

Explanation / Answer

use KE = PE

0.5 mv^2 = eV

so speed v = sqrt(2eV/m)

v = sqrt(2* 4*1.6 e-19 * 350/1.34 e-26)

v = 1.82 *10^5 m/s

so now apply centripetal force = magnetic force

i.e mv^2/r = qvB,

where m = mass o the charged particle

v = velocity,   r = radius ,

q = charge = 1.6*10^-19 C

B = magnetic field

so now , so as r    = mv/qB

B = mv/qR

B = magnetic field = (1.34 e-26 * 1.82 e 5) /(4*1.6 e-19 * 0.45)

B = 8.46 *10^-3 Tesla

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induced emf is defiend as the rate of change of magnetic flux

in mathematical form,

induced emf e = NAdB/dt    or NABW   or   NA dB/dt cos theta

where A = area

N = no. of tunrs

W = angular frequency

dB/dt = rate of change of magnetic field

so emf e = 400 * 3.14* 0.15 *0.15 (0.5-0.3)/0.25

emf e = 150.72 Volts

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