Two tiny spheres carrying charges of \(1.5\) µC and \(2.5\) µC are located \(30\) cm apart. What is the potential at a point \(10\) cm from the midpoint in a plane normal to the line and passing through the mid-point?
1. \(1.5\times 10^{5}\) V
2. \(1.0\times 10^{5}\) V
3. \(2.4\times 10^{5}\) V
4. \(2.0\times 10^{5}\) V

The diagrams below show regions of equipotential. 
    
A positive charge is moved from \(\mathrm{A}\) to \(\mathrm{B}\) in each diagram. Choose the correct statement from the options given below:

Consider a uniform electric field in the \(\mathrm{z}\)-direction. The potential is a constant:

a.	in all space.
b.	for any \(\mathrm{x}\) for a given \(\mathrm{z}.\)
c.	for any \(\mathrm{y}\) for a given \(\mathrm{z}.\)
d.	on the \(\mathrm{x-y}\) plane for a given \(\mathrm{z}.\)

Choose the correct option:

In a region, the potential is represented by \(V=(x,y,z)=6x-8xy-8y+6yz,\) where \(V\) is in volts and \(x,y,z\) are in meters. The electric force experienced by a charge of \(2\) coulomb situated at a point \((1,1,1)\) is:
1. \(6\sqrt{5}~\text{N}\)
2. \(30~\text{N}\)
3. \(24~\text{N}\)
4. \(4\sqrt{35}~\text{N}\)

In a certain region of space with volume \(0.2\) m³, the electric potential is found to be \(5\) V throughout. The magnitude of electric field in this region is:
1. \(0.5\) N/C
2. \(1\) N/C
3. \(5\) N/C
4. zero

The electric field at the origin is along the positive x-axis. A small circle is drawn with the centre at the origin cutting the axes at points \(\mathrm A\), \(\mathrm B\), \(\mathrm C\) and \(\mathrm D\) having coordinates \((a,0),(0,a),(-a,0),(0,-a)\) respectively. Out of the points on the periphery of the circle, the potential is minimum at:
1. \(\mathrm A\)
2. \(\mathrm B\)
3. \(\mathrm C\)
4. \(\mathrm D\)