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 F_0, find the time at which the force needed will be F_0 2 .

e=Bvl i= e R = Bvl 2r(l+vt) 1. F=ilB= Bvl 2r(l+vt) = B^2l^2v 2r(l+vt) 2. Just after t=0 f_0=ilB=lB ( lBv 2rl )= lB^2v 2r f_0 2 = lB^2v 4r = l^2B^2v 2r(l+vt) 2l=l+vt = l v

Consider the situation of the previous problem. 1. Calculate the …

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Question

Consider the situation of the previous problem.

Calculate the force needed to keep the sliding wire moving with a constant velocity v.
If the force needed just after $t = 0$ is $F_0$, find the time at which the force needed will be $\frac{\text{F}_0}{2}.$

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Answer

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

$\text{F}=\text{ilB}=\frac{\text{Bvl}}{2\text{r}(\text{l}+\text{vt})}\times\text{lB}=\frac{\text{B}^2\text{l}^2\text{v}}{2\text{r}(\text{l}+\text{vt})}$
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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