# Electromagnetic Induction and rectangular loop

In summary, the conversation discusses a rectangular loop and slide wire in a uniform magnetic field, with the slide wire given an initial speed and then released. Part a asks for the expression for the magnitude of the force exerted on the wire while it is moving, and part b asks for the distance the wire moves before coming to rest. The answer for part a is \frac{B^2 L^2 v}{R}, and for part b, the distance is \frac{m v_0 R}{a^2 B^2}, which can be found by separating variables and integrating.
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?

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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.

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

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.

thx so much~

## 1. What is electromagnetic induction?

Electromagnetic induction is the process by which an electric current is induced in a conductor when it is placed in a changing magnetic field.

## 2. How does a rectangular loop contribute to electromagnetic induction?

A rectangular loop is a type of conductor that is often used to demonstrate electromagnetic induction. When a changing magnetic field is passed through the loop, it creates an electric current in the loop.

## 3. What factors affect the amount of induced current in a rectangular loop?

The amount of induced current in a rectangular loop is affected by the strength of the magnetic field, the speed at which the magnetic field changes, and the size and shape of the loop.

## 4. What is Faraday's Law of Induction?

Faraday's Law of Induction states that the magnitude of the induced current in a conductor is directly proportional to the rate of change of the magnetic field passing through the conductor.

## 5. How is electromagnetic induction used in everyday life?

Electromagnetic induction has many practical applications, such as in generators and transformers used for electricity generation and distribution, induction cooktops, and electric motors. It is also used in technologies like wireless charging and magnetic levitation.

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