A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is 2Omega$2\Omega$ then the force needed to move the rod towards right with constant speed (v) of 1.5 m/s is ____ N.

### Related Formula E = B l v$E = B l v$ i = fracER$$i = \frac{E}{R}$$ F_B = i l B = fracB^2 l^2 vR$$F_{B} = i l B = \frac{B^2 l^2 v}{R}$$ ### Core Logic To maintain a constant speed, the external force applied must balance the opposing magnetic force generated by the induced current. F_textext = F_B$$F_{\text{ext}} = F_{B}$$ ### Step 1: Calculate External Force Given values: B = 0.10text T$B = 0.10\text{ T}$ l = 1text m$l = 1\text{ m}$ v = 1.5text m/s$v = 1.5\text{ m/s}$ R = 2\, Omega$R = 2\, \Omega$ F_textext = fracB^2 l^2 vR$$F_{\text{ext}} = \frac{B^2 l^2 v}{R}$$ F_textext = frac(0.10)^2 times (1)^2 times 1.52$$F_{\text{ext}} = \frac{(0.10)^2 \times (1)^2 \times 1.5}{2}$$ F_textext = frac0.01 times 1.52 = frac0.0152 = 0.0075$$F_{\text{ext}} = \frac{0.01 \times 1.5}{2} = \frac{0.015}{2} = 0.0075$$ F_textext = 7.5 times 10^-3text N$$F_{\text{ext}} = 7.5 \times 10^{-3}\text{ N}$$

### Pattern Recognition Standard "sliding rod on rails" problem. The required mechanical force to maintain terminal velocity is always F = fracB^2 L^2 vR$F = \frac{B^2 L^2 v}{R}$. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Induction