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. \(\mathrm D\)

The electric field and the electric potential at a point are E and V respectively.

(a) If E = 0, V must be zero.

(b) If V = 0, E must be zero.

(c) If E ≠ 0, V cannot be zero.

(d) If V ≠ 0, E cannot be zero

Choose the coorect option 

1. (a) only 

2. (b) , (c) 

3. (c) , (d) 

4. None of these 

The electric potential decreases uniformly from 120 V to 80 V as one moves on the x-axis from x = –1 cm to x = +1 cm. The electric field at the origin

(a) must be equal to 20 V cm^–1

(b) may be equal to 20 V cm^–1

(c) may be greater than 20 V cm^–1

(d) may be less than 20 V cm^–1

Choose the coorect option 

1. (a) only 

2. (b) , (c) 

3. (c) , (d) 

4. (a) , (d) 

The electric field in a region is directed outward and is proportional to the distance r from the origin. Taking the electric potential at the origin to be zero,

(a) it is uniform in the region

(b) it is proportional to r

(c) it is proportional to r²

(d) it increases as one goes away from the origin.

 Choose the coorect option 

1. (a) only 

2. (b) , (c) 

3. (c) only 

4. (a) , (d)