electric dipole moment problems and solutions
The dipole moment is the first term in a multipole expansion.Electric dipole moment is measured in Coulomb-meters (C m) in the SI system. At a Point on axial Line :  We have to find Electric field intensity at Point P . The electric dipole moment of a given charge distribution is a measure of the separation between the positive and negative charges in the system. Find the work done in rotating the dipole by an angle π. Torque acting on a dipole placed in a uniform electric field: Potential energy of dipole in a uniform electric field : Centre of mass & Conservation of Linear Momentum. Question: What happens when an electric dipole is placed in a non-uniform electric field? For more information, 12th physics, CBSE syllabus, CBSE NCERT solutions, CBSE Sample papers, previous year question paper of CBSE class 12 register with Takshila Learning. Thus, $ \displaystyle \vec{E} = \frac{p sin\theta}{4 \pi \epsilon_0 r^3} \, \hat{\theta} $, (iii) Potential due to a dipole at any point P(r , θ) is given by, $ \displaystyle   V = \frac{p cos\theta}{4 \pi \epsilon_0  r^2} $.

. Q: What is Ideal dipole? A sample of HCl gas is placed in a uniform electric field of magnitude 3 × 10, Electric Field and Electric Field Lines: Solved Example Problems, Torque experienced by an electric dipole in the uniform electric field, Electrostatic Potential energy and Electrostatic potential, Electrostatic potential at a point due to an electric dipole, Relation between electric field and potential, Electrostatic potential energy for collection of point charges, Electrostatic potential energy of a dipole in a uniform electric field. . English Quiz For IBPS PO , SBI PO, IBPS CLERK, SBI CLERK , RRB , SSC, India Railways, DMRC, Quant Quiz For IBPS CLERK , SBI PO, IBPS PO, SBI CLERK, SSC, RRB, DMRC, IR, Reasoning Quiz for IBPS Clerk , SBI PO, IBPS PO, SBI Clerk, RRB, General (Tips, facts, education, science related), GS Quiz For IBPS CLERK , SBI PO, IBPS PO, SBI CLERK, SSC, RRB, DMRC, IR, Indian Festivals and Important date-Short essay, National Cancer Awareness Day – 7 November, CA Final Exam Eligibility , Exams , Subjects & Syllabus. Work in groups on these problems. An atomic unit of electric dipole moment is a0e, where a0 is the radius of the first Bohr orbit for hydrogen and e is the magnitude of the electronic charge. Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail, Electric Dipole : Solved Example Problems, The position vector for the +q on the positive x-axis is ai and position vector for the +q charge the negative x axis is -a, In this case one charge is placed at the origin, so its position vector is zero. Performance & security by Cloudflare, Please complete the security check to access. An atomic unit of dipole moment is about 8.478 × 10 −29 C m. Current Affairs Calculate the electric dipole moment for the following charge configurations. • The SI units for electric dipole moment are coulomb-meter (C⋅m); however, a commonly used unit in atomic physics and chemistry is the debye (D). Note that in this case p is directed from -2q to +q. But, if the field is uniform the net force becomes zero and the torque is given by, $\large \tau = qE \times Perpendicular \; distance $, $\large \tau = (q \times 2a )E  sin\theta $, $\large \tau = pE  sin\theta $ ; where p = electric dipole moment, $ \large \vec{\tau} = \vec{p} \times \vec{E} $, Small amount of work done in rotating a dipole through small angle dθ is, Work done in rotating a dipole from θ1 to θ2 is, $\large W = \int_{\theta_1}^{\theta_2} \tau d\theta$, $\large W = \int_{\theta_1}^{\theta_2} p E sin\theta d\theta $, $\large W = p E \int_{\theta_1}^{\theta_2} sin\theta d\theta $, $\large W = p E [-cos\theta]_{\theta_1}^{\theta_2}$, $\large W = -p E [cos\theta_2 – cos\theta_1]  $, If Potential Energy is arbitrarily taken zero when dipole is at 90° , then potential energy in rotating the dipole and inclining at an angle θ is, Potential Energy ,  $\large U = -p E cos\theta  $, case(i) If θ = 0° , then U = -p E (Stable equilibrium), case(i) If θ = 180° , then U = p E (Unstable equilibrium).

So, the dipole will rotate till it becomes parallel to the electric field. Note: Discount Not Available For IFRS Course, NCERT Solutions For Class 12 physics Electric Dipole. We are Hiring 6 × 1 0 5 N C − 1 Along the dipole moment direction AB, which is … We have to find Electric field intensity at Point P . Take your favorite fandoms with you and never miss a beat. Find The Electric Field In Point P If The Electric Dipole Is Over The Z-axis And Point P Is Located With Spherical Angle 8.15 Points) This problem has been solved! Another way to prevent getting this page in the future is to use Privacy Pass. See the answer. For a collection of point charges, the dipole moment is equal to, An electric dipole placed in an electric field will experience a torque equal to, The electric potential at a point at a distance r from a dipole will be. Electric field Intensity due to an electric dipole.

The electric dipole moment is a vector quantity. τ = p E sin θ, (as for small angle ,sin θ → θ), ⇒ τ = − p E θ (If we assume angular displacement to be anti-clockwise, torque is clockwise). τmax = pE sin 90 = 3 .4×10−30 ×3 ×104 N m. Copyright © 2018-2021 BrainKart.com; All Rights Reserved. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. • Figure 2.3.1 A system of three charges Solution: Using the superposition principle, the force on q3 is 13 23 31323 2213 23 013 23 1 ˆˆ 4 qq qq πε rr FFF r r GGG In this case the second term will have a negative coefficient, since is negative. Case (c) . Calculate the maximum torque experienced by each HCl molecule. By resolving these field intensity , $\large E_{PA} sin\theta \; and \;  E_{PB} sin\theta $  will be cancel out .

Electric dipole moment is a vector quantity. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. The electric dipole moment is a vector quantity. They are placed in a uniform electric field at an angle θ with the E→ (θ ≈ 0o). Hence only the second charge +q with position vector ai contributes to the dipole moment, which is  = qa . Torque on an Electric Dipole in a Uniform Electric Field; Magnetic Dipole Moment; Electric potential due to a Dipole (V) Suppose there are two charges –q, placed at A, and +q placed a B, separated by a distance d, forming a dipole.

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An electric dipole with dipole moment p = (3.00i + 4.00j) (1.24 x 10–30 C ∙ m) in an electric field E = (4000 N/C)i. The centers of positive (H) and negative (O) charges of a water molecule lie at different points, hence it possess permanent dipole moment. $ \displaystyle \vec{E} = \frac{2p cos\theta}{4 \pi \epsilon_0 r^3}\, \hat{r} $, Along the perpendicular bisector, θ = 90 °  . The O-H bond length is 0.958 × 10-10 m due to which the electric dipole moment of water molecule has the magnitude p = 6.1 x 10-30 Cm. From both cases (a) and (b), we can infer that in general the electric dipole moment depends on the choice of the origin and charge configuration. When the dipole becomes parallel to the electric field, the rotational motion will stop. • $ \displaystyle \alpha = -\frac{p E}{I} \theta $, $ \displaystyle \omega = \sqrt{\frac{p E}{I} } $, Moment of inertia , $ \displaystyle I = M (\frac{L}{2})^2 + M (\frac{L}{2})^2 $, Time period $ \displaystyle T = \frac{2\pi}{\omega} $, $ \displaystyle T = 2\pi \sqrt{\frac{I}{p E}} $, The minimum time to required align itself is T/4 sec, Exercise : A dipole of dipole moment p→ is kept along an electric field E→ such that p→ and E→ are in the same direction. dipole moment is about 3.336 × 10 −12 C m, and a debye (D) is 10 −18 cgs esu.

The dipole moment is the first term in a multipole expansion. It is because of this reason that the electric dipole moment of an electric dipole (total charge is zero) is always directed from –q to +q, independent of the choice of the origin. Your email address will not be published. SI unit of electric dipole moment isCoulomb- meter (Cm). Your IP: 81.201.63.13 If you get stuck, try asking another group for help.

Suppose the midpoint of AB is O.

Ans: When an electric dipole is placed in a non-uniform electric field, the dipole will have both rotational and translational motion. Become Affiliate Hence only the second charge +q with position vector ai contributes to the dipole moment, which is. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. Example: Two tiny spheres, each of of mass M , and charges +q and -q respectively , are connected by a massless rod of length , L . Though this setup sounds fairly contrived, many molecules (water among them) act like dipoles, because within the molecule the charges separate leaving a net positive side and a net negative side. Electric Dipole moment: Electric dipole moment is defined as the product of magnitude of one of the charges and length of the dipole say ‘2a’ i.e.

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