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CBSE Class 12-science Answered

how do ifind electric field due to a uniformly charged ring on a point inside it
Asked by Girijeshpandey.rjil | 28 Apr, 2018, 03:24: PM
answered-by-expert Expert Answer
 
Let us consider a point P inside the ring which is at a distance a from centre O as shown in figure.
Electric field dE at P due to a small segment of ring Rdθ is given by
 
where λ = q / (2πR) is the charge density per unit length of ring and q is the total charge distributed uniformly over the ring
 
At P, we have electric field due to the various segments of wire. To find the overall electric field we have to sum up the electrical field 
contributions of all the segments. we have to consider here for electrical field contribution of each segment, there is an electrical field contribution in opposite direction due to the ring segment which is diametrically opposite to the previous segment. As shown in figure, resolved vertical componenets of these electrical fields are getting cancelled and horizontal componenets are added up. Hence we can write the relation for magnitude of electric field E as given below
Above integration does not have closed form analytical solution. Above integration can be solved only by numerical methods.
By solving the above integral by numerical methods, we can get the magnitude of electrical field for typical values of a and R

Answered by Thiyagarajan K | 04 May, 2018, 03:34: PM
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