A point charge of 0.5C is brought from infinity to a point A in free space.how much work is required to this?
To calculate the work required to bring a point charge from infinity to a specific point, you need to consider the concept of electric potential energy.
The work done in moving a point charge against an electric field is given by the change in electric potential energy (\(U\)). The equation is:
\[W = \Delta U\]
Considering the point charge (\(q\)) and the potential at infinity (\(V_{\infty}\)) to be zero, the electric potential energy (\(U\)) at point A can be calculated using the formula:
\[U = qV\]
where \(V\) is the electric potential at point A.
The electric potential (\(V\)) at a given point due to a point charge is given by:
\[V = \frac{kq}{r}\]
where \(k\) is the electrostatic constant (\(8.99 \times 10^9 \, N\cdot m^2/C^2\)) and \(r\) is the distance between the point charge and the point A.
To find the work required, you need to calculate the change in electric potential energy (\(\Delta U\)) by subtracting the electric potential energy at infinity (\(U_{\infty}\)) from the electric potential energy at point A (\(U_A\)):
\[\Delta U = U_A - U_{\infty}\]
Since \(U_{\infty} = 0\), the equation simplifies to:
\[\Delta U = U_A\]
Substituting the values:
\[\Delta U = qV\]
\[\Delta U = (0.5 \, C)(\frac{kq}{r})\]
Make sure to substitute the appropriate values for the electrostatic constant (\(k\)), charge (\(q\)), and distance (\(r\)) in order to calculate the work required to bring the point charge from infinity to the point A.