Why is Electric Potential Energy Defined in the Y-Direction Only?

[Seraph404]

My book first introduces expressions for work and energy by referring to concepts from mechanics and gravitation. It uses the familiar expressions F =mg (-y direction) & U=mgy to explain the expressions it gives for electric potential energy. However... I understand that the force due to gravity in the first couple of expressions is always downward, hence the negative y-direction. But when it gives the expressions for force and potential energy of a point charge, F_y = -q₀*E & U = q₀*E_y, I don't understsand why they define it with only the y-component. Doesn't it depend on the direction of your electric field? I mean... electric field doesn't always have to be in the y-direction, right?

 

[Seraph404]

Ah, never mind. I think it had to do with the fact that the electric field was uniform, so there was only one direction for the force to be exerted. Sorry about that.

 

[astrokreng]

Yes, you are correct. The electric field does not always have to be in the y-direction. The expressions for electric potential energy, Fy = -q0*E & U = q0*Ey, are specifically for a point charge in the y-direction. In general, the electric field and the direction of the force due to the electric field will depend on the geometry and arrangement of the charges involved. The expressions given in your book are simply specific examples and may not apply to all situations.

In order to fully understand electric potential energy, it is important to understand the concept of electric potential. Electric potential is a measure of the potential energy per unit charge at a given point in an electric field. It is a scalar quantity and is defined as the work done per unit charge to move a test charge from infinity to a given point in the electric field.

Therefore, the electric potential energy of a point charge will depend on the direction and magnitude of the electric field at that point. In general, the electric potential energy can be calculated using the expression U = q0*V, where V is the electric potential at that point.

In summary, the expressions given in your book are specific examples and may not apply to all situations. It is important to understand the concept of electric potential and how it relates to electric potential energy in order to fully understand and apply these concepts in different scenarios.