Question

Define electric potential at a point. Is it a scalar or a vector quantity? Obtain an expression for electric potential due to a point charge.

Answer 1

In an electrostatic field amount of Workdone in carrying unit positive test charge from infinity to certain point against the be electrostatic force of the field along any path between them is known as electric potential at that point.
e.g., $V_P-V_{\infty}=\frac{W_{\infty\to\ p}}{q_0}=-\int\limits^p_{\infty}\mathbb{E}.dl$
Here , p is the point where we want to find electric potential.

You noticed that electric potential is the dot product of electric field vector and position vector. So, potential must be scalar because we know dot product of any two vectors be always scalar quantity.

Electric potential expression , $V_P-V_{\infty}=\frac{W_{\infty\to\ p}}{q_0}=-\int\limits^p_{\infty}\mathbb{E}.dl$

Answer 2

the work done to bring one unit of charge from one point to the other is known as electrical potential.

it is a vector quantity.

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