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12th Class Physics Magnetism Question Bank Case Based (MCQs) - Moving Charges and Magnetism

  • question_answer
    Two charged particles A and B having the same charge, mass and speed enter into a magnetic field in such a way that the initial path of A makes an angle of \[30{}^\circ \] and that of B makes an angle of \[90{}^\circ \] with the field. Then the trajectory of:

    A) B will have smaller radius of curvature than that of A

    B) both will have the same curvature

    C) A will have smaller radius of curvature than that of B

    D) both will move along the direction of their original velocities.

    Correct Answer: A

    Solution :

    (a) B will have smaller radius of curvature than that of A Using, qv \[B\,\sin \theta =\frac{m{{v}^{2}}}{r}\] \[r\propto \frac{1}{\sin \,\theta }\] for the same values of m. v, q and B \[\therefore \frac{{{r}_{A}}}{{{r}_{B}}}=\frac{\sin \,90{}^\circ }{\sin \,30{}^\circ }=2\] or \[{{r}_{A}}=2{{r}_{B}}\] or \[{{r}_{B}}<{{r}_{A}}\]


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