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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Self Evaluation Test - Electric Chages and Fields

  • question_answer
    A rod of length 2.4 m and radius 4.6 mm carries a negative charge of \[4.2\times {{10}^{-7}}C\] spread uniformly over it surface. The electric field near the mid-point of the rod, at a point on its surface is

    A) \[-\,8.6\times {{10}^{5}}N{{C}^{-1}}\]

    B) \[8.6\times {{10}^{4}}N{{C}^{-1}}\]

    C) \[-\,6.7\times {{10}^{5}}N{{C}^{-1}}\]

    D) \[6.7\times {{10}^{4}}N{{C}^{-1}}\]

    Correct Answer: C

    Solution :

    [c] Here, \[\ell =2.4m,r=4.6mm=4.6\times {{10}^{-3}}m\] \[q=-4.2\times {{10}^{-7}}C\] Linear charge density, \[\lambda =\frac{q}{\ell }\] \[\frac{-4.2\times {{10}^{-7}}}{2.4}=-1.75\times {{10}^{-7}}C{{m}^{-1}}\] Electric field, \[E=\frac{\lambda }{2\pi {{\varepsilon }_{0}}r}\] \[=\frac{-1.75\times {{10}^{-7}}}{2\times 3.41\times 8.854\times {{10}^{-12}}4.6\times {{10}^{-3}}}\] \[=-6.7\times {{10}^{5}}N{{C}^{-1}}\]


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