Question

Positive charge Q is distributed uniformly over a circular ring of radius R . A particle having a mass m and a negative charge q, is placed on its axis at a distance x from the center. Find the force on the particle. Assume x<<<<R

Answer 1

Step 1, Given data and related figure

Charge = Q

The radius of the ring = R

Value of charge on the axis = -q

Step 2, Finding the force

As we know that electric field E at the point P due to the charged ring is given as

$E=\frac{KQx}{{(R^2+x^2)}^{\frac{3}{2}}}$

According to the question x<<<<R

So the electric field will be

$E=\frac{KQx}{R^3}$

Now we know that the force of a charge placed in the electric field is given as

$F=Q\times E$

Putting all the values

$F=\frac{q\times K\times Qx}{R^3}$

Hence the force on the charge paced at the axis is $F=\frac{q\times K\times Qx}{R^3}$