What Is the Induced EMF in a Circular Coil at t = 5 s?

AI Thread Summary
The discussion revolves around calculating the induced EMF in a circular coil with 35 turns and a diameter of 19 cm placed in a time-varying magnetic field. The magnetic field is defined as B(t) = 6t^2 + 6t + 2 T, and the induced EMF is determined using the formula E = -NAB/dt. A participant initially calculated the EMF as 36.12 V but later realized the error may stem from using the diameter instead of the radius for area calculations. The correct approach involves ensuring proper unit conversions and applying the formula accurately, with the derivative of the magnetic field being dB/dt = 12t + 6. The discussion emphasizes the importance of these calculations and confirms that a negative voltage can occur in this context.
Liketothink
Messages
68
Reaction score
0

Homework Statement

A circular coil with 35 turns of wire and a diameter of 19 cm is placed in a magnetic field given by B(t) = 6 t^2 + 6 t + 2 T where t is time in seconds. The field is perpendicular to the plane of the coil. What is the induced EMF at t = 5 s?

Homework Equations

E=-d(magnetic flux)/dtime

The Attempt at a Solution


I found E to be 36.12 V but that's wrong. I'm not sure what's wrong. I did E=NAB/time.
 
Last edited:
Physics news on Phys.org
Emf is proportional to negative the derivative or rate of change of the magnetic flux with respect to time. The area is constant, thus
V = -NA*dB/dt.
 
I plugged in -36.12 but it's still wrong. Can we have a negative voltage?
 
Could you please tell me where I'm wrong? I have a couple of hours left.
 
dB/dt = 12t + 6; at t = 5s, dB/dt = 66T/s
N = 35 turns
A = pi*r^2...so your problem might be that you're using the diameter of 19cm instead of the radius; also, be sure that you convert the given units to the proper units, so the radius = d/2 = 9.5cm = .095m.
The emf is V = -NA*dB/dt...and you could have a negative voltage.
 
Thank you very much I appreciate it.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Why is the value of EMF generated by a generator not zero at t = 0 s?
Replies
2
Views
1K
Induced EMF in a moving Loop Conductor
Replies
3
Views
2K
Faraday's law help -- Induced EMF vs. time graph
Replies
7
Views
2K
Calculate the induced EMF of a rotating loop
Replies
7
Views
3K
What is the amplitude of induced EMF in a magnetic dipole antenna?
Replies
3
Views
2K
Need someone to check my equations and work on this induced EMF problem
Replies
1
Views
1K
Induced EMF graph of a very small wire moving through a coil
Replies
3
Views
2K
EMF induced in a coil encircling an ideal solenoid
Replies
2
Views
2K
The Magnitude of Induced EMF in a Moving Rod?
Replies
8
Views
4K
Induced EMF in a coil outside a solenoid
Replies
15
Views
7K

Hot Threads

Recent Insights

Back
Top