JEE Main · 2014 · 06 Apr 2014 · Offline · Electrostatics

Assume that an electric field

E = 30 x^{2} \hat{i}

exists in space. Then the potential difference

V_{A} - V_{O}

, where

V_{O}

is the potential at the origin and

V_{A}

the potential at

x = 2 m

is:

(A)-80 V✓ Correct
(B)80 V
(C)120 V
(D)-120 V

Answer: (A)

Solution

The field is

E = 30 x^{2} \hat{i}

, and potential difference follows from

d V = - E \cdot d x

. Integrating from the origin out to

x = 2 m

V_{A} - V_{O} = - \int_{0}^{2} 30 x^{2} d x = - 30 [\frac{x ^{3}}{3}]_{0}^{2} = - 30 \times \frac{8}{3} = - 80 V

. The quantity asked for is a potential difference, so its unit is the volt; the paper printed the choices in joules, which is a misprint corrected here to volts. The required value is

- 80 V

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option

Practise more: all JEE Main PYQs on Electrostatics →

More JEE Main questions on Electrostatics

Six point charges are kept 60° apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the centre of the circle is ______.
( $ϵ_{0}$ is permittivity of free space)
JEE Main 2026View solution →
Electric field in a region is given by $E = A x \hat{i} + B y \hat{j}$ , where $A = 10 V / m^{2}$ and $B = 5 V / m^{2}$ . If the electric potential at a point $(10, 20)$ is 500 V , then the electric potential at origin is ____ V.
JEE Main 2026View solution →
Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :
JEE Main 2026View solution →
Five positive charges each having charge $q$ are placed at the vertices of a pentagon as shown in the figure. The electric potential ( $V$ ) and the electric field ( $E$ ) at the center O of the pentagon due to these five positive charges are:
JEE Main 2026View solution →
Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is :
JEE Main 2026View solution →
Two shorts dipoles $(A, B)$ , A having charges $\pm 2 μ C$ and length 1 cm and $B$ having charges $\pm 4 μ C$ and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point $P$ , equi-distant from the …
JEE Main 2026View solution →