Negative sign in Faraday's Law With Faraday's law, is it standard convention to leave off the negative sign? Or are answers with negative EMF acceptable (generally speaking)?
 A: It is not a convention.It just means that induced emf opposes the  magnetic flux passing thriugh the closed loop.
Emf can be negative because it is defined as the amount of work done by an external mechanism on a unit charge to displace it from one position to another.
A: The simple form of Faraday's law is $\mathcal E = - \dfrac{d\phi}{dt}$ where $\mathcal E$ is the induced emf in a loop and $\dfrac{d\phi}{dt}$ is the rate of change of magnetic flux though the loop.  
 
In the left-hand diagram the magnetic flux is $BA$ and it is increasing so the induced current, $I_{\rm induced}$, must try and produce a downward magnetic field and reduce the rate of change of flux (Lenz).
The direction of the induced current is shown in the diagram and it is the induced emf, $\mathcal E$, which is responsible for driving the current in that direction.
Going though all this I have not really made any use of the negative sign.  
One of Maxwell's laws, $\displaystyle \oint_{\rm loop} \vec E \cdot d\vec s = - \dfrac{d}{dt} \iint_{\rm area} \vec B\cdot d\vec a $, is based on Faraday's laws.  
The $\displaystyle \iint_{\rm area} \vec B\cdot d\vec a $ term is the flux passing through the area bounded by the loop and $\hat n$ is the unit vector which is at right angles to the area bounded by the loop (normal) and $d\vec a = da \,\hat n$ and so $\displaystyle \iint_{\rm area} \vec B\cdot \hat n\,  da$.  
The dot product gives the component of the magnetic field which is at right angles to the area.  
So you have minus the rate of change of flux on the right hand side of the equation.  
The left hand side of Maxwell's equation requires the evaluation of a line integral.
Whichever way you go around the loop, clockwise or anticlockwise looking from above, the magnitude of the line integral will be the same but the direction will determine the sign of the line integral.
There is a convention when doing line integrals linked to surface integrals.
The direction of the unit vector $\hat n$ is linked to the direction in which the line integral needs to be evaluated by the right hand rule.
Direction of curled fingers of the right hand point in direction of line integral and the thumb points in the direction of the unit vector.
The right hand diagram shows this.  
The left hand side of the equation $\displaystyle \oint_{\rm loop} \vec E \cdot d\vec s$ is the emf which is induced in the loop.
Now suppose $vec B$ is increasing in magnitude.
This will mean that the rate of change of flux is positive. 
If the Maxwell equation had been $\displaystyle \oint_{\rm loop} \vec E \cdot d\vec s = \color {red}+ \,\dfrac{d}{dt} \iint_{\rm area} \vec B\cdot d\vec a $ then this would have meant that since the right hand side is positive the left hand side must also be positive and the induced current would flow in the direction shown in the right hand diagram.
This is obviously incorrect.  
A negative sign is introduced into the equation to correctly predict the direction of the induced emf produced by the changing magnetic flux.
A: Emf can't be negative. Actually the negative sign in Faraday's law show that the emf is induced in such a way that  it opposes the cause of it.
Suppose you have a close loop of a conducting wire and you place it in a region where magnetic field is increasing perpendicular to the plane of the wire. So according to the Faraday's law,  the induced emf or current will oppose the increasing field by generating its own field in opposite direction.
If the field was decreasing then it will oppose the decrease by generating its own field in the same direction.
This is the significance of negative sign.
A: I you connect an AC source to an inductor and resistor in series, you will find that the back emf is positive, thus opposing the AC source.
