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# Electric Fields

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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