When electric dipole is placed in uniform electric field

Case study question of Physics – Electric charges and field

Case study 4:- When electric dipole is placed in uniform electric field, its two charges experience equal and opposite forces, which cancel each other and hence net forceon electric dipole in uniform electric field is zero. However, these forces are not collinear, so they give rise to some torque on the dipole. Since, net force on electric dipole in uniform electric field is zero, so no work is done in moving the electric dipole in uniform electric field. However, some work is done in rotating the dipole against the torque acting on it.

Potential difference (ΔV) between two points A and B separated

Read the given passage carefully and give the answer of the following questions:

Q 1:- The dipole moment of a dipole in a uniform external field $\vec{E}$ is $\vec{P}$ . What will be the torque $\vec{\Tau}$ acting on the dipole ?

Q 2:- An electric dipole consists of two opposite charges. Each of magnitude 1.0 μC separated by a distance of 2.0 cm. The dipole is placed in an external field of $10^5 NC^{-1}$ . What is the maximum torque on the dipole ?

Q 3:- Torque on a dipole in uniform electric field is minimum when θ is equal what angle ?

Q 4:- When an electric dipole is held at an angle in a uniform electric field, what are the net force F and torque τ on the dipole ?

Q 5:- What is the net force on electric dipole in uniform electric field ?

Answer :- 1. As, τ = either force × perpendicular distance between the two forces

⇒ τ = q E × 2a sin θ or τ = PE sin θ

OR τ $= \vec{P} \times \vec{E}$ [Since, q(2a) = P]

2. The maximum torque on the dipole in an external electric field is given by

τ = PE = q(2a) × E

Here, q = 1 μC = $10^{-6}$ C, 2a = 2 cm = $2 \times 10^{-2}$ m

$E = 10^5 nC^{-1}$ , τ = ?.

τ $= 10^{-6}\times 2 \times 10^{-2} \times 10^5 = 2\times 10^{-3}$ Nm

3. When θ is 0° or 180°, τ is minimum, which means the dipole moment should be parallel to the direction of the uniform electric field.

4. Net force is zero and torque acts on the dipole, trying to align p and E

5. Zero

Case study 1:- A charge is a property associated with the matter due to which it experiences and produces an electric and magnetic fields. Charges are scalar in nature and they add up like real numbers. Also, the total charge of an isolated system is always conserved. When the objects rub against each other, charges acquired by them must be equal and opposite.

Read the given passage carefully and give the answer of the following questions:

Q 1:- The cause of charging is:

(a) The actual transfer of protons

(b) The actual transfer of electrons

(d) None of the above

Answer :- See all answer

Case study 2:- Coulamb’s law states that the electrostatic force of attraction or repulsion acting between two stationary points charges is given by

$F = \dfrac{1}{4\pi \epsilon _0}\dfrac{q_1q_2}{r^2}$

Where F denotes the force between two charges $q_1$ and $q_2$ separated by a distance r in free space, $\epsilon _0$ is a constant known as permittivity of free space. Free space is vacuum and may be taken to be air practically.

If free space is replaced by a medium, then $\epsilon _0$ is repaced by $(\epsilon _0 k)$ or $\epsilon _0 \epsilon$ , where k is known as dielectric constant or relative permittivity.

Read the given passage carefully and give the answer of the following questions:

Q 1:- In coulamb’s law, $F = k\dfrac{q_1 q_2}{r^2}$ , then on which of the following factors does the proportionality constant k depends ?

(a) Electrostatic force acting between the two charge

(b) Nature of the medium between the two charges

(d) Distance between the two charges

Answer :- See the answer

Case study 3:- Animals emit low frequency electric fields due to a process known as osmoregulation. This process allows the concentration of ions (charged atoms or molecules) to flow between the inside of our bodies and the outside. In order for our cells to stay intact, the flow of ions needs to be balanced. But balanced doesn’t necessarily mean equal. The concentration of ions within a shrimp’s body is much lower than that of the sea water it swims in. Their voltage or potential sifference generated between the two concentrations across ‘leaky’ surfaces, can then be measured.

Read the given passage carefully and give the answer of the following questions:

Solution:- See full solution

Case study 5:- Surface charge density is defined as charge per unit surface area of surface charge distribution i.e., σ = dq/ds. Two large thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite sign having magnitude of $17.0\times 10^{-22}$ C/m² as shown. The intensity of electric field at a point is $E =\dfrac{\sigma}{\epsilon_0}$ , where $\epsilon _0=$ permittivity of free space.