Why is electric field at the centre of a disc not 0?
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The electric field at any point at a finite distance z from the centre of a charged disc of uniform charge density along the axis of the disc is given by the equation:
E=∫dE=σz4ϵ0∫R0(z2+r2)−3/2(2r)dr=σ2ϵ0(1−zz2+R2−−−−−−√)E=∫dE=σz4ϵ0∫0R(z2+r2)−3/2(2r)dr=σ2ϵ0(1−zz2+R2)
According to this equation, at z=0z=0, the electric field is :
E=σ2ϵ0E=σ2ϵ0
However, logically, I feel that at the centre of the disc, the field must be zero as all the field vectors get cancelled at that point. Why does this happen?
E=∫dE=σz4ϵ0∫R0(z2+r2)−3/2(2r)dr=σ2ϵ0(1−zz2+R2−−−−−−√)E=∫dE=σz4ϵ0∫0R(z2+r2)−3/2(2r)dr=σ2ϵ0(1−zz2+R2)
According to this equation, at z=0z=0, the electric field is :
E=σ2ϵ0E=σ2ϵ0
However, logically, I feel that at the centre of the disc, the field must be zero as all the field vectors get cancelled at that point. Why does this happen?
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