Question

Two charges \[ + 3.2 \times {10^{ - 19}}C\] and \[ - 3.2 \times {10^{ - 19}}C\] placed at \[2.4\mathop A\limits^ \circ \] apart from an electric dipole. It is placed in a uniform electric field of intensity \[4 \times {10^5}V/m\]. The electric dipole moment is
A. \[15.36 \times {10^{ - 29}}Cm\]
B. \[15.36 \times {10^{ - 19}}Cm\]
C. \[7.68 \times {10^{ - 29}}Cm\]
D. \[7.68 \times {10^{ - 19}}Cm\]

Answer 1

Hint:A dipole is the combination of two charges of equal in magnitude and opposite in nature. The electric dipole moment is proportional to the magnitude of the charge and the separation between the charges.

Formula used:
\[p = qd\]
Here p is the magnitude of the dipole moment, q is the magnitude of charge separated at distance d.

Complete step by step solution:
It is given that two charges are \[ + 3.2 \times {10^{ - 19}}C\] and \[ - 3.2 \times {10^{ - 19}}C\].
\[{Q_1} = + 3.2 \times {10^{ - 19}}C\]
\[\Rightarrow {Q_2} = - 3.2 \times {10^{ - 19}}C\]
The separation between the charges is \[2.4\mathop A\limits^ \circ \]. As we know that the angstrom is the unit of distance.One angstrom is equal to \[{10^{ - 10}}m\]. We need to convert the given distance unit into S.I. unit.

So, the distance between the charges in S.I. unit is,
\[d = 2.4 \times {10^{ - 10}}m\]
The magnitude of the charge is equal to \[3.2 \times {10^{ - 19}}C\].
\[q = 3.2 \times {10^{ - 19}}C\]
Using the formula to find the magnitude of the electric dipole moment,
\[p = qd\]
Here, p is the magnitude of the electric dipole moment, q is the magnitude of the charge separated by the distance d.

The magnitude of the dipole moment is,
\[p = \left( {3.2 \times {{10}^{ - 19}}C} \right) \times \left( {2.4 \times {{10}^{ - 10}}} \right)Cm\]
\[\therefore p = 7.68 \times {10^{ - 29}}Cm\]
Hence, the magnitude of the electric dipole moment is \[7.68 \times {10^{ - 19}}Cm\]. The electric dipole moment is a vector quantity, so the electric dipole moment is represented using the magnitude of the electric dipole moment as well the direction of the electric dipole moment.

Therefore, the correct option is C.

Note: As the electric field lines due to negative point charge is directed towards the charge and the electric field lines due to positive point charge is directed away from the charge. So the direction of the electric dipole moment is assumed to be from positive charge to the negative charge.