Qstnid -Iv-37-consider The Situation Of The Previous Problem. (A) Calculate The Force Needed To Keep The Sliding Wire Moving With A Constant Velocity V. (B) If The Force Needed Just After T = 0 Is F0, Find The Time At Which The Force Needed Will Be F0/2. (A) Calculate The Force Needed To Keep The Sliding Wire Moving With A Constant Velocity V. (B) If The Force Needed Just After T = 0 Is F0, Find The Time At Which The Force Needed Will Be F0/2. - 38: Electromagnetic Induction

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NEET-XII-Physics

38: Electromagnetic Induction

with Solutions - page 9

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#37
Consider the situation of the previous problem. (a) Calculate the force needed to keep the sliding wire moving with a constant velocity v. (b) If the force needed just after t = 0 is F₀, find the time at which the force needed will be F₀/2. (a) Calculate the force needed to keep the sliding wire moving with a constant velocity v. (b) If the force needed just after t = 0 is F₀, find the time at which the force needed will be F₀/2.
Ans : Emf induced in the circuit, e = Bvl
Current in the circuit, `` i=\frac{e}{R}=\frac{Bvl}{2r(l+vt)}`` (a) Force F needed to keep the sliding wire moving with a constant velocity v will be equal in magnitude to the magnetic force on it. The direction of force F will be along the direction of motion of the sliding wire.
Thus, the magnitude of force F is given by
`` F=ilB=\frac{Bvl}{2r(l+vt)}\times lB``
`` =\frac{{B}^{2}{l}^{2}v}{2r(l+vt)}`` (b) The magnitude of force F at t = 0 is given by
`` {F}_{0}=ilB=lB\left(\frac{lBv}{2rl}\right)``
`` =\frac{l{B}^{2}v}{2r}...\left(1\right)``
Let at time t = T, the value of the force be F₀/2.
Now,
`` \frac{{F}_{0}}{2}=\frac{{l}^{2}{B}^{2}v}{2r(l+vT)}``
On substituting the value of F₀from (1), we get
`` \frac{l{B}^{2}v}{4r}=\frac{{l}^{2}{B}^{2}v}{2r(l+vT)}``
`` \Rightarrow 2l=l+vT``
`` \Rightarrow T=\frac{l}{v}``
Page No 309: (a) Force F needed to keep the sliding wire moving with a constant velocity v will be equal in magnitude to the magnetic force on it. The direction of force F will be along the direction of motion of the sliding wire.
Thus, the magnitude of force F is given by
`` F=ilB=\frac{Bvl}{2r(l+vt)}\times lB``
`` =\frac{{B}^{2}{l}^{2}v}{2r(l+vt)}`` (b) The magnitude of force F at t = 0 is given by
`` {F}_{0}=ilB=lB\left(\frac{lBv}{2rl}\right)``
`` =\frac{l{B}^{2}v}{2r}...\left(1\right)``
Let at time t = T, the value of the force be F₀/2.
Now,
`` \frac{{F}_{0}}{2}=\frac{{l}^{2}{B}^{2}v}{2r(l+vT)}``
On substituting the value of F₀from (1), we get
`` \frac{l{B}^{2}v}{4r}=\frac{{l}^{2}{B}^{2}v}{2r(l+vT)}``
`` \Rightarrow 2l=l+vT``
`` \Rightarrow T=\frac{l}{v}``
Page No 309:

#37-a
Calculate the force needed to keep the sliding wire moving with a constant velocity v.
Ans : Force F needed to keep the sliding wire moving with a constant velocity v will be equal in magnitude to the magnetic force on it. The direction of force F will be along the direction of motion of the sliding wire.
Thus, the magnitude of force F is given by
`` F=ilB=\frac{Bvl}{2r(l+vt)}\times lB``
`` =\frac{{B}^{2}{l}^{2}v}{2r(l+vt)}``

#37-b
If the force needed just after t = 0 is F₀, find the time at which the force needed will be F₀/2.
Ans : The magnitude of force F at t = 0 is given by
`` {F}_{0}=ilB=lB\left(\frac{lBv}{2rl}\right)``
`` =\frac{l{B}^{2}v}{2r}...\left(1\right)``
Let at time t = T, the value of the force be F₀/2.
Now,
`` \frac{{F}_{0}}{2}=\frac{{l}^{2}{B}^{2}v}{2r(l+vT)}``
On substituting the value of F₀from (1), we get
`` \frac{l{B}^{2}v}{4r}=\frac{{l}^{2}{B}^{2}v}{2r(l+vT)}``
`` \Rightarrow 2l=l+vT``
`` \Rightarrow T=\frac{l}{v}``
Page No 309: