Imagine that you have a circular conducting ring that you can expand and contrac
ID: 1509286 • Letter: I
Question
Imagine that you have a circular conducting ring that you can expand and contract. Let's call its radius r and its electrical resistance R = 10 . It is oriented horizontally, perpendicular to a uniform magnetic field that points upwards with a magnitude of 0.1 T. You smoothly reduce its radius from 10 cm to 5 cm over a time interval of 5 s, with constant dr/dt.
(a) As viewed from above, what is the direction of the induced current in the ring (clockwise or counterclockwise)? Explain your answer.
(b) At the instant that you begin contracting the ring (when it has a radius of 10 cm), how large is the induced current that flows around it? How does this induced current change as you continue to contract it – does it get larger, or smaller, or remain the same?
(c) At the instant that you begin contracting the ring, how large is the magnetic force that acts on it?
Explanation / Answer
let,
mass of the person, m=66kg
hight of the stair, h=22cm
a)
enegry, E1=m*g*h
E1=66*9.8*(0.22)
E1=142.296 J
b)
E2=2*m*g*h
E2=2*66*9.8*(0.22)
E2=284.592 J
magnetic field, B=0.1 T
resistance, R=10 ohms
radius, r=10cm to 5cm
time interval, dt=5sec
a)
direction of induced current is counter-clockwise
b)
i=emf/R
i=B(dA/dt)R
i=(B/R)*(pi*r*dr/dt)
i=(0.1/10)*(pi*0.1*(10-5)*10^-2/5)
i=3.1416*10^-5 A
i=31.42*10^-6 A
i=31.42 uA
--->
current gets larger if you continue to contract it,
c)
F=i*L*B
F=(31.42*10^-6)*(2pi*r)*B
F=(31.42*10^-6)*(2pi*0.1)*0.1
F=1.97*10^-6 N