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

Answer:

The loop penetrate 4 cm into the magnetic field.

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

$\epsilon =1\times2\times5\times10^{-2}$

$\epsilon =10\times10^{-2}\ volt$

We need to calculate the current

Using Lenz's formula

$i=\dfrac{\epsilon}{R}$

$i=\dfrac{10\times10^{-2}}{20\times10^{-3}}$

$i=5\ A$

We need to calculate the force

Using formula of force

$F=i(\vec{w}\times\vec{B})$

$F=iwB$

Put the value into the formula

$F=5\times5\times10^{-2}\times2$

$F=0.5\ N$

We need to calculate the acceleration

Using formula of acceleration

$a=\dfrac{F}{m}$

Put the value in to the formula

$a=\dfrac{0.5}{40\times10^{-3}}$

$a=12.5\ m/s^2$

We need to calculate the distance

Using equation of motion

$v^2=u^2+2as$

$s=\dfrac{v^2-u^2}{2a}$

$s=\dfrac{0-1^2}{2\times(-12.5)}$

$s=0.04\ m$

$s=4\ cm$

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