6 × 1 0 5 N C − 1 Along the dipole moment direction AB, which is … View 5 Recommendations 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 electric dipole consists of two charges of opposite signs separated by a small distance. 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. The electric dipole moment of a given charge distribution is a measure of the separation between the positive and negative charges in the system. The electric dipole moment  is directed from center of negative charge to the center of positive charge, as shown in the figure. Ans: When an electric dipole is placed in a non-uniform electric field, the dipole will have both rotational and translational motion. Your IP: 81.201.63.13 HOW TO SCORE 100/100 MARKS IN CBSE CLASS 10 MATHS BOARD EXAMS? The following results can be established for a dipole.

Cloudflare Ray ID: 5ec48d057db9edaf When the dipole becomes parallel to the electric field, the rotational motion will stop. The net charge on an electric dipole is zero. Hence only the second charge +q with position vector ai contributes to the dipole moment, which is  = qa .

. The electric dipole moment of a given charge distribution is a measure of the separation between the positive and negative charges in the system. The Attempt at a Solution I thought dipole moment would be zero because there is no dipole in the system.+2q and -q can not make a dipole because for … Suppose the midpoint of AB is O. Homework Equations In the simple case of two point charges, one with charge +q and the other one with charge −q, the electric dipole moment p is: where d is the displacement vector pointing from the negative charge to the positive charge.

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. The total force on an electric dipole placed in a uniform electric field is zero.

Electric field  Intensity at a Point P due to A(-q) is, $\large E_{PA} = \frac{1}{4\pi \epsilon_0} \frac{q}{AP^2}$, $\large E_{PA} = \frac{1}{4\pi \epsilon_0} \frac{q}{(r+a)^2}$ (along $\vec{PA}$), Electric field  Intensity at a Point P due to B(+q) is, $\large E_{PB} = \frac{1}{4\pi \epsilon_0} \frac{q}{BP^2}$, $\large E_{PB} = \frac{1}{4\pi \epsilon_0} \frac{q}{(r-a)^2}$ (along $\vec{BP} \; produced $). $\large E = E_{PA} cos\theta + E_{PB} cos\theta $, $\large E = 2 \frac{1}{4\pi \epsilon_0}\frac{q}{(r^2 + a^2)}.
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6 × 1 0 5 N C − 1 Along the dipole moment direction AB, which is … View 5 Recommendations 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 electric dipole consists of two charges of opposite signs separated by a small distance. 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. The electric dipole moment of a given charge distribution is a measure of the separation between the positive and negative charges in the system. The electric dipole moment  is directed from center of negative charge to the center of positive charge, as shown in the figure. Ans: When an electric dipole is placed in a non-uniform electric field, the dipole will have both rotational and translational motion. Your IP: 81.201.63.13 HOW TO SCORE 100/100 MARKS IN CBSE CLASS 10 MATHS BOARD EXAMS? The following results can be established for a dipole.

Cloudflare Ray ID: 5ec48d057db9edaf When the dipole becomes parallel to the electric field, the rotational motion will stop. The net charge on an electric dipole is zero. Hence only the second charge +q with position vector ai contributes to the dipole moment, which is  = qa .

. The electric dipole moment of a given charge distribution is a measure of the separation between the positive and negative charges in the system. The Attempt at a Solution I thought dipole moment would be zero because there is no dipole in the system.+2q and -q can not make a dipole because for … Suppose the midpoint of AB is O. Homework Equations In the simple case of two point charges, one with charge +q and the other one with charge −q, the electric dipole moment p is: where d is the displacement vector pointing from the negative charge to the positive charge.

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. The total force on an electric dipole placed in a uniform electric field is zero.

Electric field  Intensity at a Point P due to A(-q) is, $\large E_{PA} = \frac{1}{4\pi \epsilon_0} \frac{q}{AP^2}$, $\large E_{PA} = \frac{1}{4\pi \epsilon_0} \frac{q}{(r+a)^2}$ (along $\vec{PA}$), Electric field  Intensity at a Point P due to B(+q) is, $\large E_{PB} = \frac{1}{4\pi \epsilon_0} \frac{q}{BP^2}$, $\large E_{PB} = \frac{1}{4\pi \epsilon_0} \frac{q}{(r-a)^2}$ (along $\vec{BP} \; produced $). $\large E = E_{PA} cos\theta + E_{PB} cos\theta $, $\large E = 2 \frac{1}{4\pi \epsilon_0}\frac{q}{(r^2 + a^2)}.
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electric dipole moment problems and solutions


electric dipole moment problems and solutions




τmax = pE sin 90 = 3 .4×10−30 ×3 ×104 N m. Copyright © 2018-2021 BrainKart.com; All Rights Reserved. Maximum value of torque acting on the dipole is when Ɵ = 90. Dipole moment vector is directed from the negative to the positive charge. You can also view our CBSE NCERT solutions to enhance your chances of scoring good marks in exams. 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). Electric potential due to a Dipole (V) Solution: Let us assume there are two charges, –q, fixed at point A, and +q fixed at point B. 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. For each of the following, determine if the molecule would have a dipole moment (polar or nonpolar): Here, p = 1 0 − 5 C × 5 × 1 0 − 3 m = 5 × 1 0 − 8 C m E = 2. Consider AB is an electric dipole having mid point O & length 2a  . So, the dipole will rotate till it becomes parallel to the electric field. Become A Teacher $\large E_{PA} = \frac{1}{4\pi \epsilon_0} \frac{q}{r^2 + a^2}$ (along $\vec{PA}$), $\large E_{PB} = \frac{1}{4\pi \epsilon_0} \frac{q}{r^2 + a^2}$ (along $\vec{BP} \; produced $). \frac{a}{\sqrt{r^2 + a^2}} $, $\large E = 2 \frac{1}{4\pi \epsilon_0}\frac{q \times 2a}{(r^2 + a^2)^{3/2}} $, $\large E = 2 \frac{1}{4\pi \epsilon_0}\frac{p}{(r^2 + a^2)^{3/2}} $, $\large E = 2 \frac{1}{4\pi \epsilon_0}\frac{p}{r^3} $, Note : The angle between electric field Intensity & dipole moment is 180°, Electric field due to the dipole at point P (r,θ)is given by, $ \displaystyle \vec{E} = \frac{2p cos\theta}{4 \pi \epsilon_0 r^3}\, \hat{r} + \frac{p sin\theta}{4 \pi \epsilon_0 r^3} \, \hat{\theta} $    ; where r >> a. Electric dipole moment of an electric dipole is defined as the product of the magnitude of either charge and the dipole length.

The dipole moment of each HCl molecule is 3.4 × 10-30 Cm. where p = 2 a q is the magnitude of the dipole moment.The direction of electric field on the dipole axis is always along the direction of the dipole moment vector (i.e., from − q t o q). Dipole Moment , $\large \vec{p} = (q \times 2a) \hat{i}$. Case (c) . Electric Dipole: A system containing two equal and opposite charges separated by a finite distance is called an electric dipole. dipole moment is about 3.336 × 10 −12 C m, and a debye (D) is 10 −18 cgs esu. Electric dipole moment is measured in Coulomb-meters (C m) in the SI system.

Case (a) 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 i ^ . At a Point on axial Line :  We have to find Electric field intensity at Point P . The Electric potential due to a dipole at any point P, such that OP = r will be: Show transcribed image text . Dipole Moment , $\large \vec{p} = (q \times 2a) \hat{i}$ Dipole moment vector is directed from the negative to the positive charge.

An atomic unit of dipole moment is about 8.478 × 10 −29 C m. Calculate the electric dipole moment for the following charge configurations.

Note that in this case p is directed from -2q to +q. As torque is proportional to ‘θ’ and oppositely directed, the motion will be an angular S.H.M. Your email address will not be published. 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. 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. Another way to prevent getting this page in the future is to use Privacy Pass. The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity.

$\large E = \frac{q}{4\pi \epsilon_0} [\frac{1}{(r-a)^2} – \frac{1}{(r+a)^2}] $, $\large E = \frac{q}{4\pi \epsilon_0} [\frac{(r+a)^2 – (r-a)^2}{(r^2-a^2)^2} ] $, $\large E = \frac{q}{4\pi \epsilon_0} [\frac{4 r a}{(r^2-a^2)^2} ] $, $\large E = \frac{1}{4\pi \epsilon_0} [\frac{(q \times 2a) 2 r}{(r^2-a^2)^2} ] $, $\large E = \frac{1}{4\pi \epsilon_0} [\frac{ 2 p r}{(r^2-a^2)^2} ] $ (Where q × 2a = p = dipole moment), $\large E = \frac{1}{4\pi \epsilon_0} [\frac{2 p}{r^3} ] $, Note : The angle between Electric field intensity & dipole moment is 0°. 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.

Consider an electric dipole placed in a uniform electric field of strength E.The net electric force is zero but a torque is experienced by the dipole. 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. Physics: Problems and Solutions is a FANDOM Lifestyle Community. Example: Two tiny spheres, each of of mass M , and charges +q and -q respectively , are connected by a massless rod of length , L . EXAMPLE 1.10. The water molecule (H2O) has this charge configuration. The maximum torque experienced by the dipole is when it is aligned perpendicular to the applied field. It is characterised by dipole moment vector . Become Affiliate . 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} $. Statement of a problem № 36591 next . $ \mathbf{p}(\mathbf{r}) = \iiint\limits_{V} \rho(\mathbf{r})\, (\mathbf{r}-\mathbf{r}_0) \ d V, $, $ \mathbf{p}(\mathbf{r}) = \sum_{i=1}^N \, q_i \, (\mathbf{r}_i - \mathbf{r}_0 ) $, $ \boldsymbol{\tau} = \bold{p} \times \bold{E} $, $ V(\mathbf{r}) = \frac{1}{4 \pi \epsilon_0} \frac{\hat{\mathbf{r}} \cdot \mathbf{p}}{\mathbf{r}^2} $. Your email address will not be published. But for one special case, the electric dipole moment is independent of the origin. Physics notes for class 12 : Then go through our Class 12 Physics online classes designed specifically keeping in mind the latest pattern of question papers in the CBSE exams.We also offer sample papers, Physics notes, previous question papers for Class 12 for CBSE. 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). As both the electric field intensity are in opposite direction . You should try to answer the questions without referring to your textbook. The "internal" electric field vector, meanwhile, is parallel but in the opposite direction of both the dipole moment vector and the "external" electric field dipole. Cloudflare Ray ID: 5ec48d1799072778 Calculate the maximum torque experienced by each HCl molecule.

6 × 1 0 5 N C − 1 Along the dipole moment direction AB, which is … View 5 Recommendations 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 electric dipole consists of two charges of opposite signs separated by a small distance. 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. The electric dipole moment of a given charge distribution is a measure of the separation between the positive and negative charges in the system. The electric dipole moment  is directed from center of negative charge to the center of positive charge, as shown in the figure. Ans: When an electric dipole is placed in a non-uniform electric field, the dipole will have both rotational and translational motion. Your IP: 81.201.63.13 HOW TO SCORE 100/100 MARKS IN CBSE CLASS 10 MATHS BOARD EXAMS? The following results can be established for a dipole.

Cloudflare Ray ID: 5ec48d057db9edaf When the dipole becomes parallel to the electric field, the rotational motion will stop. The net charge on an electric dipole is zero. Hence only the second charge +q with position vector ai contributes to the dipole moment, which is  = qa .

. The electric dipole moment of a given charge distribution is a measure of the separation between the positive and negative charges in the system. The Attempt at a Solution I thought dipole moment would be zero because there is no dipole in the system.+2q and -q can not make a dipole because for … Suppose the midpoint of AB is O. Homework Equations In the simple case of two point charges, one with charge +q and the other one with charge −q, the electric dipole moment p is: where d is the displacement vector pointing from the negative charge to the positive charge.

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. The total force on an electric dipole placed in a uniform electric field is zero.

Electric field  Intensity at a Point P due to A(-q) is, $\large E_{PA} = \frac{1}{4\pi \epsilon_0} \frac{q}{AP^2}$, $\large E_{PA} = \frac{1}{4\pi \epsilon_0} \frac{q}{(r+a)^2}$ (along $\vec{PA}$), Electric field  Intensity at a Point P due to B(+q) is, $\large E_{PB} = \frac{1}{4\pi \epsilon_0} \frac{q}{BP^2}$, $\large E_{PB} = \frac{1}{4\pi \epsilon_0} \frac{q}{(r-a)^2}$ (along $\vec{BP} \; produced $). $\large E = E_{PA} cos\theta + E_{PB} cos\theta $, $\large E = 2 \frac{1}{4\pi \epsilon_0}\frac{q}{(r^2 + a^2)}.

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