Q. 634.3( 6 Votes )

# Consider a circul

Answer :

**Given:**Radius of the circular ring: r

Linear charge density : λ

Distance of a point from the center of the ring : x

From the diagram we can see that,

Point P is at a distance x from the center of the ring.

Point P is at a distance of from the surface of the ring: r’ =

Circumference of the ring is : L = 2π r

**Formula used:**

We can see that, Electric field as p is resolved into vertical and horizontal components. As the ring is symmetric, vertical components are cancelled out and horizontal components add.

Thus E

_{net}=Ecosθ , where θ is the angle between x and .

We know that,

Where, λ is the linear charge density, Q is the Total charge due to whole ring and L is the circumference of the ring.

Potential at a point due to charge Q is:

k is a constant and k= =9× 10

^{9}Nm

^{2}C

^{-2}. q is the point charge.

If we substitute value of k then:

Hence, Electric potential at a point x from the center of the ring is .

Net electric field at P is Ecosθ and

From the figure:

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