Twelve point charges each of charge \(q\) C are placed at the circumference of a circle of radius \(r\) m with equal angular spacing. If one of the charges is removed, the net electric field (in N/C) at the centre of the circle is:
(\(\varepsilon_0 \)-permittivity of free space)
1. \(\frac{13q}{4\pi \varepsilon_0r^2}\)
2. zero
3. \(\frac{q}{4\pi \varepsilon_0r^2}\)
4. \(\frac{12q}{4\pi \varepsilon_0r^2}\)

A spherical conductor of radius \(10~\text{cm}\) has a charge of \(3.2 \times 10^{-7}~\text{C}\) distributed uniformly. What is the magnitude of the electric field at a point \(15~\text{cm}\) from the center of the sphere? \(\frac{1}{4\pi \varepsilon _0} = 9\times 10^9~\text{N-m}^2/\text{C}^2\)
1. \(1.28\times 10^{5}~\text{N/C}\)
2. \(1.28\times 10^{6}~\text{N/C}\)
3. \(1.28\times 10^{7}~\text{N/C}\)
4. \(1.28\times 10^{4}~\text{N/C}\)

A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance \(r\) from the centre: