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A particle of charge q moves with velocity vec(v) along positive y - direction in a magnetic field vec(B). Compute the Lorentz force experienced by the particle (a) when magnetic field is along positive y-direction (b) when magnetic field points in positive z -direction (c ) when magnetic field is in zy - plane and making an angle theta with velocity of the particle. Mark the direction of magnetic force in each case. |
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Answer» SOLUTION :Velocity of the PARTICLE is `vec(v) = v hat(j)` (a) Magnetic field is along positive y-direction, this implies, `vec(B) = v hat(j)` From Lorentz force, `vec(F_(m)) = q(v hat(j) xx B hat(j) ) ` = 0 So, no force acts on the particle when it moves along the direction of magnetic field. (b) Magnetic field points in positive z - direction, this implies, `vec(B) = B hat(K)` From Lorentz force, ` vec(F_(m)) = q (v hat(j) xx B hat(k)) = "qvB"hat(i)` Therefore, the magnitude,of the Lorentz force is qvB and direction is along positive x - direction . (c ) Magnetic field is in ZY - plane and making an angle `theta` with the velocity of the particle , which implies `vec(B) " B cos" theta aht(j) + ` B sin `theta hat(k)` From Lorentz force, `vec(F_(m)) = q(v hat(j)) xx (B cos theta hat(j) + B sin theta hat(k))` = qvBsin `theta hat(i)`  
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