# Find Potential at Point P: Electric Potential

• tony873004
In summary, the potential at point P with coordinates x=1.5 m, y=3.5 m is -54 V. This can be determined by using the dot product of the electric field vector, which is (16 V/m, 8.5 V/m), and the displacement vector from the origin to point P, which is (1.5 m, 3.5 m). This yields a result of -54 V.
tony873004
Gold Member
If $$\overrightarrow E = \left( {16\,{\rm{V/m}}} \right)\,{\rm{\hat i + }}\left( {{\rm{8}}{\rm{.5 V/m}}} \right){\rm{\hat j}}$$ and the potential is 0 at the origin, find the potential at point P with coordinates x=1.5 m, y=3.5 m.

I made a diagram. (each tick mark = 2 units). I imagine this is just a uniform electric field. The equipotential lines are perpendicular to the field lines. The two lines going up and to the right are field lines, and the two perpendicular lines are lines of equipotential. The one passing through the origin is 0V. The other one is passing through the point (1.5, 3.5), but I don't know its value. Don't I need to know how far away the charge is that is creating the Electric field in order to determine how potential will change with distance?

You can set this up as a line integral (if you're doing calculus based physics). That is, pick your path ($\vec{r}(t)=(1.5t,3.5t,0)$ with $0\le t\le1$ would be a good one) and use

$$V_f-V_i=-\int \vec{E}\circ d\vec{r}$$.

I don't understand that.

I'm still stuck on this. All I can think to do is compute the magnitude of the electric field: sqrt(16^2 + 8.5^2), and the distance from point P to the origin: sqrt(1.5^2 + 3.5^2), and since V=Ed, multiply them together which gives me 70V. But the answer in the back of the book is -54V.

I got it! It's dot product of E*V, not regular old multiplication of |E|*|V| which is what I was doing. Now I get -54 like the back of the book.

## What is electric potential?

Electric potential is the amount of electric potential energy per unit charge at a certain point in an electric field. It is a measure of the work needed to move a unit charge from the reference point to the point in question.

## How is electric potential measured?

Electric potential is measured in units of volts (V) using a voltmeter. It can also be calculated using the equation V = W/q, where V is the potential difference, W is the work done, and q is the charge.

## What is the difference between electric potential and electric potential energy?

Electric potential is the potential energy per unit charge at a point, while electric potential energy is the potential energy of a charged object in an electric field. Electric potential is a scalar quantity, while electric potential energy is a vector quantity.

## How does distance affect electric potential?

The electric potential at a point decreases as the distance from the source charge increases. This is because the electric field strength decreases with distance, and electric potential is directly proportional to the electric field strength.

## Can electric potential be negative?

Yes, electric potential can be negative. This indicates that the potential energy of a charged object at that point is negative, which means that work must be done to move the object away from that point.

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