# 25 a 125 μ c particle with a mass of 280x10 5 kg

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22.25 A 12.5- μ C particle with a mass of 2.80x10-5 kg moves perpendicular to a 1.01-T magnetic field in a circular path of radius 26.8 m. (a) How fast is the particle moving? (b) How long will it take the particle to complete one orbit? We know that Radius of the circular path r = m v / q B ==> The velocity of the particle is v = q B r / m = 12.5 x 10-6 * 1.01 * 26.8 / 2.80 x 10-5 = 12.08 m/s The time taken t = 2 * pi * r / v = 2 * 3.14 * 26.8 / 12.08 = 13.92 s 22.28 An alpha particle (the nucleus of a helium atom) consists oftwo protons and two neutrons and a mass of 6.64e-27kg. A horizontalbeam of alpha particles is injected with a speed of 2.1e5 m/s intoa regoin with a vertical magnetic feild of magnitude .175 T. a) How long does it take for an alpha particle to move halfwaythrough a complete circle?

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b)If the speed of the alpha particle is tripled , does the time found in part (a)increase, decrease, or stay the same? Why? 22.34 The long, thin wire shown in the figure is in a region of constant magnetic field . The wire carries a current of 6.2 and is oriented at an angle of 7.5 to the direction of the magnetic field.
If the magnetic force exerted on this wire per meter is 3.5 × 10 2 , what is the magnitude of the magnetic field? F / L = I B sin(theta) B = (F/L) / [ I sin(theta)] = (0.035 N/m) / [ (6.2 A) sin (7.5deg)] = 0.0432 N / (A m) At what angle will the force exerted on the wire per meter be equal to 1.4 × 10 2 ? F/L = 0.012 N/m = I B sin(theta) sin(theta) = (F/L) / (IB) = (0.014 N/m) / (6.2 A * 0.0432 T) = 0.0522 theta = 2.99 deg 22.36 A high voltage power line carriers a current of 110Amps at alocation where the Earths magnetic field is 5.9 x 10^-5 Telsapoints North 72 degrees below the horizontal. Find

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