A 1 m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is 5 $$\Omega$$, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m s$$^{-1}$$ will be _______ $$\times 10^{-3}$$ N.

Given: $$l = 1$$ m, $$B = 0.15$$ T, $$R = 5$$ $$\Omega$$, $$v = 4$$ m/s.

EMF induced: $$\varepsilon = Blv = 0.15 \times 1 \times 4 = 0.6$$ V

Current: $$I = \frac{\varepsilon}{R} = \frac{0.6}{5} = 0.12$$ A

Force needed to maintain constant speed (against the magnetic braking force):

$$F = BIl = 0.15 \times 0.12 \times 1 = 0.018 \text{ N} = 18 \times 10^{-3} \text{ N}$$

The force needed is 18 $$\times 10^{-3}$$ N.