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    Magnetic field

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    1) What is the initial direction of deflection for the charged particles entering the magnetic fields as shown in figure 1.
    (a and b)
    2) What are the strength and direction of the magnetic field at point P in figure 2?

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    Problem 1

    Force experienced by a charged particle (charge q) entering a uniform magnetic field B with a velocity v is given by :

    F = q(v X B) .......(1) where v X B represents the cross (vector) product of the velocity and magnetic field vectors.

    Magnitude of the force is given by : F = qvB sinθ where θ = angle between vectors v & B

    The force is perpendicular to the plane in which the vectors lie and points in the direction as given by the right hand rule of vector multiplication viz. curl the fingers of the right hand with the thumb stretched out such that the fingers point in the direction from the first vector towards the second vector through the smaller angle between them (that is from v towards B), then the force vector will point in the direction of the thumb.

    Case a
    x x x x x x x
    x F x x x x x x
    x x x x x x x Uniform magnetic field into the plane
    + x x x x x x ...

    Solution Summary

    Detailed solution with diagrams provided to highlight the underlying principles.