A charged particle moving through a magnetic field at right angles to the field

Question

A charged particle moving through a magnetic field at right angles to the field with a speed of 27.7 m/s experiences a magnetic force of 2.98 times 10^4 N. Determine the magnetic force on an identical particle when it travels through the same magnetic field with a speed of 5.94 m/s at an angle of 26.2 degree relative to the magnetic field. 00155 How does the magnetic force acting on a charged particle moving through a magnetic field depend on the charge of the particle, speed of the particle, magnitude of the magnetic field, and the direction the particle is traveling through the magnetic field? For this problem, why have we not been given values for the charge on the particles and the magnetic field? N Using appropriate technology, you determine that Earth's magnetic field at your location has a magnitude of 5.10 times 10^-5 T and is directed north at an angle of 59 degree below the horizontal. You charge a metallic projectile and fire it north with a speed of 616 m/s and at an angle of 14 degree above the horizontal. Determine the sign (+or-) and charge of the projectile, if the magnetic force on the projectile is 3.17 times 10^-10 N, directed due west. C

Explanation / Answer

F = q (v x B)

F = q v B sin(theta)

2.98 x 10^-4 = (q B) (27.7) sin90

qB = 1.0758 x 10^-5

now F' = q v' B sin(26.2)

F' = (1.0758 x 10^-5) (5.94) (sin26.6)

F' = 2.86 x 10^-5 N ........Ans

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11. B = 5.10 x 10^-5 ( cos59j - sin59k)

v = 616 (cos14j + sin14k)

F = - 3.17 x 10^-10 N i

F = q (v x B)

- 3.17 x 10^-10 i = q ( 5.10 x 616 x 10^-5) ( 0.125i + 0.832i)

q = - 10.5 x 10^-9 C ...........Ans

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