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An infinite number of charges each q are placed in the x-axis at distances of 1, 2, 4, 8, ………meter from the origin. If the charges are alternately positive and negative find the intensity of electric field at origin. |
Answer» Solution :The electric field intensities due to positive CHARGES at origin is away from the charges and due to -Ve charges the field intensity is towards the charges  The resultant intensity at the origin `E = E_(1) - E_(2) + E_(3) - E_(4)`...... `E= (Q)/(4pi in_(0))(1 - (1)/(2^(2)) + (1)/(4^(2)) - (1)/(8^(2))+ ......)` Since the expression in the bracket is in GP with a COMMON RATIO `=(-1)/(2^(2)) = (-1)/(4)` `E= (Q)/(4pi in_(0))(1)/([1-((-1)/(4))])= (Q)/(4pi in_(0)).(4)/(5)` `E= (4)/(5).(Q)/(4pi in_(0))` `E= (Q)/(5pi in_(0))` |
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