Question

A rectangular loop of wire with width w = 5 cm, length L = 10cm, mass m = 40 g, and resistance R = 20 mΩ has an initial velocity v0 = 1 m/s to the right. It crosses from a region with zero magnetic field to a region with B = 2T pointing out of the page. How far does the loop penetrate into the magnetic field?

Answer 1

The loop penetrate 4 cm into the magnetic field.

Step-by-step explanation:

Given that,

Width w= 5 cm

Length L= 10 cm

mass m = 40 g

Resistance R = 20 mΩ

Initial velocity = 1 m/s

Magnetic field = 2 T

We need to calculate the induced emf

Using formula of emf

`\epsilon=v_(0)Bw`

Put the value into the formula

`\epsilon =1*2*5*10^(-2)`

`\epsilon =10*10^(-2)\ volt`

We need to calculate the current

Using Lenz's formula

`i=(\epsilon)/(R)`

`i=(10*10^(-2))/(20*10^(-3))`

`i=5\ A`

We need to calculate the force

Using formula of force

`F=i(\vec{w}*\vec{B})`

`F=iwB`

Put the value into the formula

`F=5*5*10^(-2)*2`

`F=0.5\ N`

We need to calculate the acceleration

Using formula of acceleration

`a=(F)/(m)`

Put the value in to the formula

`a=(0.5)/(40*10^(-3))`

`a=12.5\ m/s^2`

We need to calculate the distance

Using equation of motion

`v^2=u^2+2as`

`s=(v^2-u^2)/(2a)`

`s=(0-1^2)/(2*(-12.5))`

`s=0.04\ m`

`s=4\ cm`

Hence, The loop penetrate 4 cm into the magnetic field.