The dipole is released from rest at θ=90.0^∘ . What is its angular speed when it reaches θ=0 ?[

step 1 Hi, in the given problem there is a uniform electric field. Suppose it is in the horizontal dire

The dipole is released from rest at θ=90.0^∘ . What is its...

Key Concepts

Conservation of Energy

This fundamental principle states that the total energy in an isolated system remains constant. For a dipole rotating in an electric field, the decrease in potential energy due to alignment with the field is exactly balanced by the increase in rotational kinetic energy, allowing one to solve for the angular speed.

Rotational Kinetic Energy

In rotational motion, the kinetic energy of an object is given by (1/2)I?², where I is the moment of inertia and ? is the angular speed. This concept is crucial when relating the work done by electric forces on a dipole to its resulting rotational kinetic energy.

Work-Energy Principle

This principle asserts that the work done by forces on a system results in a change in the system’s energy. For an electric dipole, the work done by the electric forces on the individual charges leads to a conversion of potential energy into kinetic energy, which can be calculated to determine the angular speed.

Electric Dipole

An electric dipole consists of two equal and opposite electric charges separated by a fixed distance. Its behavior in an electric field, such as experiencing a torque that tends to align it with the field, is central to understanding how forces act on distributed charges.

Transcript

00:02 Hi, in the given problem there is a uniform electric field.

00:06 Suppose it is in the horizontal direction.

00:10 In this electric field, a dipole has been kept perpendicular.

00:18 This is the dipole length, means the rod, whose ends are having these charges.

00:27 The magnitude of electric field is 200 newton per coulum.

00:32 The dipole charges are plus minus q is equal to plus minus 3 .0 microculum.

00:44 The angle between electric field and electric dipole moment is given as 90 degree.

00:52 And the mass of the charge particles, let it be small m, is given as 5 .0 gram and mass of the rod is given as 20.

01:07 0 gram capital n an angle here is 90 degree the dipole length d is equal to 7 .0 centimeter so first of all we will find the torque experienced by this dipole because this positive charge will be experiencing a force q into e towards right -hand side means in the direction of electric field and this negative charge will be experiencing the same force but in a direction opposite to the electric field so the tor is having an expression q e d sine theta so plugging in all known values for charge this is 3 .0 into 10 dash per 6 coulame electric field 2 .0 into 10 dash par 4 newton per coulang for d this is 7 .0 centimeter or 7 .0 into 10 dash per minus 2 meter and sign 90 degree so finally this torque here comes out to be 4 .2 into 10 dash par minus 3 newton into meter in a clock wise direction now we find inertia of rotation first of all for the charge particles let it be i1 and that will be given by the mass of the charge particle multiplied by the square of its distance from the axis of rotation.

02:52 And as there are two charge particles, so it will come out to be two times of m into d by 2 to the whole square.

03:00 So plugging in, known values here, for mass, this is 5 gram or 5 into 10 -dh -per -minus 3 -gram...

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