| 1. 1 $m\cfrac{dv}{dt}=mg-F_{L2}$ | 0.30 |
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| 1. 2 $F_{L1}=qv_{rot}B$ | 0.20 |
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| 1. 3 $v_{rot}=\omega r$ | 0.20 |
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| 1. 4 $m\cfrac{dv}{dt}=mg-q\omega rB$ | 0.20 |
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| 1. 5 $I\cfrac{d\omega}{dt}=M_{L1}$ | 0.30 |
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| 1. 6 $M_{L1}=qvBr$ | 0.20 |
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| 1. 7 $I=mr^2$ | 0.20 |
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| 1. 8 $v=dh/dt$ | 0.20 |
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| 1. 9 $I\omega=qBrh$ | 0.40 |
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| 1. 10 $mg=qBr\omega_0$ | 0.40 |
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| 1. 11 $mgh_0=\cfrac{mv^2_{max}}{2}+\cfrac{I\omega_0^2}{2}$ | 0.30 |
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| 1. 12 $v_{max}=\cfrac{mg}{qB}$ | 0.30 |
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| 2. 1 $m\cfrac{d^2h}{dt^2}=mg-\cfrac{(qB)^2}{m}h$ | 0.30 |
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| 2. 2 $\omega_L=\cfrac{qB}{m}$ | 0.20 |
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| 2. 3 $\Delta t=\cfrac{\pi}{2\omega_L}=\cfrac{\pi m}{2qB}$ | 0.30 |
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| 3. 1 $h_{max}=2h_0=\cfrac{2gm^2}{q^2B^2}$ | 0.20 |
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| 4. 1 $m\cfrac{dv}{dt}=mg-F_L$ | 0.30 |
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| 4. 2 $F_L=BIL$ | 0.20 |
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| 4. 3 $L=2\pi r$ | 0.20 |
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| 4. 4 $\mathscr{E}=\cfrac{d\Phi}{dt}=BLv$ | 0.30 |
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| 4. 5 $\mathscr{E}=IR$ | 0.30 |
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| 4. 6 $R=\rho L/s$ | 0.20 |
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| 4. 7 $v_0=\cfrac{mg\rho}{2\pi r sB^2}$ | 0.30 |
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| 5. 1 $\cfrac{mR}{BL}\cfrac{dI}{dt}=mg-BIL$ | 0.20 |
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| 5. 2 $I(0)=0$ | 0.20 |
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| 5. 3 $A_1=\cfrac{mg}{2\pi rB}$ | 0.20 |
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| 5. 4 $B_1=-\cfrac{mg}{2\pi rB}$ | 0.20 |
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| 5. 5 $\gamma_1=-\cfrac{2\pi rsB^2}{m\rho}$ | 0.20 |
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| 6. 1 $\mathscr{E}-\cfrac{q}{C}=IR$ | 0.30 |
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| 6. 2 $C=\varepsilon_0 s/\delta$ | 0.20 |
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| 6. 3 $I=\cfrac{dq}{dt}$ | 0.20 |
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| 6. 4 $a_0=\cfrac{g}{1+\cfrac{B^2(2\pi r)^2\varepsilon_0 s}{m\delta}}$ | 0.30 |
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| 7. 1 $BL\cfrac{dv}{dt}=\cfrac{I}{C}+R\cfrac{dI}{dt}$ | 0.50 |
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| 7. 2 $R\cfrac{dI}{dt}=gBL-\left(\cfrac{1}{C}+\cfrac{B^2L^2}{m}\right)I$ | 0.50 |
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| 7. 3 $I(0)=0$ | 0.10 |
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| 7. 4 $A_2=\cfrac{2\pi rg\varepsilon_0 sB}{\delta\left(1+\cfrac{B^2(2\pi r)^2\varepsilon_0 s}{m\delta}\right)}$ | 0.30 |
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| 7. 5 $B_2=\cfrac{2\pi rg\varepsilon_0 sB}{\delta\left(1+\cfrac{B^2(2\pi r)^2\varepsilon_0 s}{m\delta}\right)}$ | 0.30 |
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| 7. 6 $\gamma_2=-\left(1+\cfrac{B^2(2\pi r)^2\varepsilon_0 s}{m\delta}\right)\cfrac{\delta}{2\pi r\rho\varepsilon_0}$ | 0.30 |
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