Electric fields describe the interaction of stationary charged matter. They underlie the working of diverse technology from atom smashers to the poor cell reception you're getting right now.

Find the **electrostatic force of interaction** between two parallel non conducting wires each of length \(l\) , charge density per unit length \(\lambda\), and separated by a distance \(d\).

Give your answer as the value of this force in \(\text{ Newtons }\) using \( \lambda = 10 \mu \text{C/ m}\), \( l = 1 \text{m} \), \(\text{ d = 1m }, \frac{1}{4 \pi \epsilon_{0} } = 9 \times 10^9\text{ N } m^2/ C^2 \)

**Note**:

The wires completely face each other (like if their equations were \(0 \leq x \leq L, y,z= 0\) and \(0 \leq x \leq L, y= d, z=0\))

**in meters per second** of the charge located at C.

Evaluate \(a+b\).

**Details and Assumptions:**

\(\hat{k} \) is the unit vector along the direction of \(z\) axis in a normal right handed Cartesian coordinate system.

Reference potential i.e. \( (V=0) \) is obviously the sphere since it is grounded.

\(R\) is the radius of the sphere.

The particle is released, and flies toward the disc. Find the velocity (in **m/s**) of the particle when it has covered half the distance.

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