Question

Write the vector form of torque acting on the electric dipole moment. Mention the SI unit of torque acting on the dipole placed in the uniform electric field. What are electric field lines?

Answer 1

Hint: Make use of the definition of torque and and the concept of electric dipole moment to solve this. Torque is the moment of force that is the tendency to rotate the body on which is applied.

Complete step by step solution:
An electric dipole is an arrangement of opposite amounts that has equal to electric charges, separated by fixed distance for this the condition is the amount will be different that is positive and negative.
Electric Dipole Moment: The electric dipole moment. This moment can be defined as the separation of positive and negative electrical charges within a system. By this one can measure the overall polarity of the system. The SI unit of electric dipole moment is coulomb meter (cm)which is known as Debye (D) which is also a vector form of torque.
When any physical quantity has direction and magnitude it is called a vector. In electricity when two currents meet at a function the resultant current of these will be a vector scum. In vector form torque is the cross product of the radius vector and the force vector.
\[\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}\]
When torque is the cross product of lever radius and force,
\[\overrightarrow{\tau }=|\overrightarrow{r}|\times |\overrightarrow{a|}\text{sin }\!\!\theta\!\!\text{ }\]
It’s the product of force and its perpendicular distance from the lever’s fulcrum
So, from above
\[\overrightarrow{r}\times \overrightarrow{F}=|\overrightarrow{r}|\times |\overrightarrow{a|}\operatorname{Sin}\theta \]
S.I unit of torque is Newton meter.

Electric field lines:
These lines are visualizing vector fields; they have a pattern of lines referred to as electric field lines. These lines are directed away from positively source change to negatively change source an electric field line is a curve that is drawn in such a way that the tangent of if at each point is in direction of the net field.

Note:Electric field near the change is high and when we go further it decreases because the electric field is inversely proportional to the square of the distance.