Question

class 12 ... plz answer .....

a charge of 4×10 to power -9 C is distributed uniformly over the circumference of a conducting ring of radius 0.3 m .Calculate the ring at 0.4 m from its center and also at the center .

Ans :- 115.2 N/C ; Zero​

Answer 1

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Given :-

♣ Radius of the ring(r) = 0.3 m

♣ Charge on the ring(q) = 4*10⁻⁹ C

♣ x = 0.4 m

To find :-

The ring at 0.4 m from its center and also at the center.

Solution :-

Expression for the electric field at a point on the axis of the ring at distance x from the centre of the ring is given as :

$\displaystyle{\sf{E_x=\frac{qx}{4\pi \epsilon_0(x^2+r^2)^\frac{3}{2} } }}\\\\\\\displaystyle{\sf{\longrightarrow E_x=\frac{9*10^9*4*10^-^9*0.4}{(0.4^2+0.3^2)^\frac{3}{2} } }}\\\\\\\displaystyle{\sf{\longrightarrow E_X=\frac{14.4*2}{(0.5)^2} }}\\\\\\\displaystyle{\sf{\longrightarrow E_X=\frac{28.8}{0.25} }}\\\\\\\displaystyle{\sf{\boxed{\longrightarrow E_X=115.2\ N/C}}}$

Now, at the centre of the ring,

$\displaystyle{\sf{E_x=\frac{qx}{4\pi \epsilon_0(x^2+r^2)^\frac{3}{2} } }}$

Here, r = 0

So, $\boxed{\sf{E_X=0}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Hope this answer helps you.☺