Question

Find the electric field a distance z above the center of a square loop (side a) carrying uniform line charge λ

Answer 1

Answer:

take a look at the below pic

Explanation:

Answer 2

Answer:

The electric field at distance z above the center of a square loop carrying uniform line charge λ,

E (edge) =   (1 / 4πε₀) × ( λα / $\sqrt{z^{2} + \frac{a^{2} }{4} }$$\sqrt{(z^{2} + \frac{a^{2} }{4}) +\frac{a^{2} }{4} }$

Explanation:

To find the electric field a distance z above the center of a square loop (side a) carrying uniform line charge λ.

First we need to find the electric field of one edge by using the result of,

Where ,

E = 4E cosθ

E = (1 / 4πε₀) × $\frac{q}{r^{2} }$

Where q = λ a

E =  (1 / 4πε₀) × (λ a/r) × z

E =  (1 / 4πε₀) × (λ a/r) × Cosθ z

By simplifying the above equation we get,

E = (1 / 4πε₀) × ( 2λ L / z $\sqrt{z^{2} +L^{2} }$ ) ₓ z

We know that,

L ⇒ (a/2)

z ⇒  $\sqrt{z^{2} + \frac{a^{2} }{4} }$

So, the electric field at one edge will be:

E (edge) =   (1 / 4πε₀) × ( λα / $\sqrt{z^{2} + \frac{a^{2} }{4} }$ $\sqrt{(z^{2} + \frac{a^{2} }{4} )+\frac{a^{2} }{4} }$ )

 

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