Electromagnetic Induction and rectangular loop

[adrian116]

the question is that:
A rectangular loop with width L and a slide wire with mass m are as shown in Fig. A uniform magnetic field $\vec B$ is directed perpendicular to the plane of the loop into the plane of the figure. The slide wire is given an initial speed of $v_0$ and then released. There is no friction between the slide wire and the loop, and the resistance of the loop is negligiblein comparison to the resistance R of the slide wire. a) Obtain an expression for F, the magnitude of the force exerted on the wire while it is moving at speed v. b). Show that the distance x that the wire moves before coming to rest is $\frac{m v_0 R}{a^2 B^2}$

i have done part a ,
the ans. is $\frac{B^2 L^2 v}{R}$
but for part b ,
i can just calculate half of the value of x mentioned in the question.
i did it in this way

subt. F from a to $F=ma$ to find the acceleration
then subt. the ans. to
$v^2=u^2+2as$ by taking v=0 and u=v.
is there any mistake?

 

[OlderDan]

the question is that:
A rectangular loop with width L and a slide wire with mass m are as shown in Fig. A uniform magnetic field $\vec B$ is directed perpendicular to the plane of the loop into the plane of the figure. The slide wire is given an initial speed of $v_0$ and then released. There is no friction between the slide wire and the loop, and the resistance of the loop is negligiblein comparison to the resistance R of the slide wire. a) Obtain an expression for F, the magnitude of the force exerted on the wire while it is moving at speed v. b). Show that the distance x that the wire moves before coming to rest is $\frac{m v_0 R}{a^2 B^2}$

i have done part a ,
the ans. is $\frac{B^2 L^2 v}{R}$
but for part b ,
i can just calculate half of the value of x mentioned in the question.
i did it in this way

subt. F from a to $F=ma$ to find the acceleration
then subt. the ans. to
$v^2=u^2+2as$ by taking v=0 and u=v.
is there any mistake?

You have a force that is proportional to the velocity. As the wire slows, the force diminishes. You cannot use the initial acceleration as a constant.

 

[adrian116]

then , what should i do , can u give me some hints?

 

[OlderDan]

then , what should i do , can u give me some hints?

F = ma = mdv/dt = m(dv/dx)(dx/dt) = mvdv/dx

You can separate variables and integrate.

 

[adrian116]

thx so much~