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Electromagnetic Induction — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsElectromagnetic Induction5 Marks
Question
Consider the situation of the previous problem.
  1. Calculate the force needed to keep the sliding wire moving with a constant velocity v.
  2. If the force needed just after t = 0 is F0, find the time at which the force needed will be $\frac{\text{F}_0}{2}.$
✓

Answer

$\text{e}=\text{Bvl}$

$\text{i}=\frac{\text{e}}{\text{R}}=\frac{\text{Bvl}}{2\text{r}(\text{l}+\text{vt})}$

  1. $\text{F}=\text{ilB}=\frac{\text{Bvl}}{2\text{r}(\text{l}+\text{vt})}\times\text{lB}=\frac{\text{B}^2\text{l}^2\text{v}}{2\text{r}(\text{l}+\text{vt})}$
  2. Just after $\text{t}=0$

$\text{f}_0=\text{ilB}=\text{lB}\Big(\frac{\text{lBv}}{2\text{rl}}\Big)=\frac{\text{l}\text{B}^2\text{v}}{2\text{r}}$

$\frac{\text{f}_0}{2}=\frac{\text{l}\text{B}^2\text{v}}{4\text{r}}=\frac{\text{l}^2\text{B}^2\text{v}}{2\text{r}(\text{l}+\text{vt})}$

$\Rightarrow2\text{l}=\text{l}+\text{vt}$

$\Rightarrow\text{T}=\frac{\text{l}}{\text{v}}$

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