Question

The distance of point P on the axis from the centre of an uniformly charged circular ring is maximum, is 2$^{-n}$ R (radius of a ring is R). Value of 'n' is : ​

Answer 1

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Let us consider a small charge element of charge dq

And, dq= 2πRQThe field at point P due to this element is=E= r 2KdqE= (R 2+x2)Kdq

Now, from figure we see that component of field normal to axis is cancelled by two diametrically opposite points.

Hence, only component of field along axis is left which add up for all such elements.

E net =∫Ecosθ where θ is same for all elements means θ=constant

⟹E net=∫ (R 2+x 2Kcosθdq⟹E net= (R 2+x2)KQ cosθ⟹E net= (R 2+x 2 )KQ

R 2 +x 2x⟹E net

= (R 2+x 2) 3/2KQx

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Answer 2

Answer:

Let us consider a small charge element of charge dq

And, dq= 2πRQThe field at point P due to this element is=E= r 2KdqE= (R 2+x2)Kdq

Now, from figure we see that component of field normal to axis is cancelled by two diametrically opposite points.

Hence, only component of field along axis is left which add up for all such elements.

E net =∫Ecosθ where θ is same for all elements means θ=constant

⟹E net=∫ (R 2+x 2Kcosθdq⟹E net= (R 2+x2)KQ cosθ⟹E net= (R 2+x 2 )KQ

R 2 +x 2x⟹E net

= (R 2+x 2) 3/2KQx