\(PQ\) is an infinite conductor carrying a current \(I\). \(AB\) and \(CD\) are smooth conducting rods on which a conductor \(EF\) moves with constant velocity \(v\) as shown. The resistance of the resistor is \(R\).

Find the magnitude of force in Newton needed to maintain constant speed of \(EF\).

**Details and assumptions:**

- \(I=10\text{ A}\)
- \(b = 20\text{ m}\)
- \(a = 2\text{ m}\)
- \(v = 10\frac{\text{m}}{\text{s}}\)
- \(R=10\;\Omega\)
- Take the volumetric susceptibility of the medium surrounding the system to be 0.
- Multiply the magnitude of force by \(10^{12}\) and then report the answer.
- Give answer to 3 decimal places.

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