Point charges Q1=1kNl, Q2=1nC, Q3=-1kNl, Q4=-1kNl

The coordinates of point charges Q1=1kNl, Q2=1nC, Q3=-1kNl, Q4=-1kNl are specified by radius vectors r1=(0,0), r2=(a,0), r3=(a,a), r4= (0,a) on the lattice plane, where the cell has the shape of a square with side a=0.1 m. There are no charges in the remaining lattice nodes.

To determine the dipole moment of a system of charges, it is necessary to find the vector sum of the products of charges and the radius vector of each charge. Thus, the dipole moment of this system of charges is equal to:

p = Q1 * r1 + Q2 * r2 + Q3 * r3 + Q4 * r4

p = (1kNl) * (0.0) + (1nC) * (a.0) + (-1kNl) * (a.a) + (-1kNl) * (0.a)

p = (-1kNl, 1kNl)

To determine the potential energy (P) of a system of charges in an external electric field (E = 0.1 V/m), you need to use the formula:

П = Σ(Qi * φi)

where Qi is the charge of each charge, and φi is the potential created by the charges.

In this case, the potential φi at a point with coordinates r can be found using the formula:

φi = k * Qi / |r - ri|

where k is the Coulomb constant, and ri is the radius vector of the i-th charge.

Then the potential energy of the system of charges P is equal to:

П = k * (Q1 * φ1 + Q2 * φ2 + Q3 * φ3 + Q4 * φ4)

П = k * (Q1 / |r - r1| + Q2 / |r - r2| + Q3 / |r - r3| + Q4 / |r - r4|)

P = (9 * 10^9 N * m^2 / Cl^2) * [(1kNl) / |r| + (1nC) / |r - (a,0)| + (-1kNl) / |r - (a,a)| + (-1kNl) / |r - (0,a)|]

where |r|, |r - (a,0)|, |r - (a,a)| and |r - (0,a)| - distances between point r and charges Q1, Q2, Q3 and Q4, respectively.

Using formulas, you can calculate the dipole moment of a system of charges and its potential energy in an external electric field E = 0.1 V/m.

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Our product is a unique digital product that includes a description of point charges Q1=1kNl, Q2=1kNl, Q3=-1kNl, Q4=-1kNl. These charges are located on a plane at lattice nodes with a cell in the shape of a square with side a=0.1 m. The lattice nodes in which these charges are located are specified by radius vectors r1=(0.0), r2=(a.0 ), r3=(a,a), r4=(0,a). There are no charges in the remaining nodes.

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This product is a description of a system of point charges Q1=1kNl, Q2=1nC, Q3=-1kNl, Q4=-1kNl, located on a plane at lattice nodes with a square-shaped cell with side a=0.1 m. Lattice nodes, in which the indicated charges are located are specified by radius vectors r1=(0,0), r2=(a,0), r3=(a,a), r4=(0,a). There are no charges in the remaining nodes.

Using this description, you can calculate the dipole moment of a system of charges, which is equal to the vector sum of the products of charges and the radius vector of each charge, that is, p = Q1 * r1 + Q2 * r2 + Q3 * r3 + Q4 * r4, which gives the result (-1kNl , 1kNl).

You can also find the potential energy P of a system of charges in an external electric field E = 0.1 V/m, using the formula P = k * (Q1 / |r - r1| + Q2 / |r - r2| + Q3 / |r - r3 | + Q4 / |r - r4|), where k is the Coulomb constant, and ri is the radius vector of the i-th charge. When substituting numerical values, we obtain P = (9 * 10^9 N * m^2 / Cl^2) * [(1kNl) / |r| + (1nC) / |r - (a,0)| + (-1kNl) / |r - (a,a)| + (-1kNl) / |r - (0,a)|]. Here |r|, |r - (a,0)|, |r - (a,a)| and |r - (0,a)| - distances between point r and charges Q1, Q2, Q3 and Q4, respectively.

Thus, this product allows you to better understand the physical phenomena associated with electric charges and obtain specific numerical values ​​of the dipole moment and potential energy of a system of charges in an external electric field. The description is presented in a beautifully designed html format, which makes it easy to read and study the information, as well as easy to save and share it with others.

This product is a unique digital product containing a description of point charges Q1=1kNl, Q2=1nC, Q3=-1kNl, Q4=-1kNl, located on a plane at lattice nodes with a square-shaped cell with side a=0.1 m and specified by radius vectors r1=(0,0), r2=(a,0), r3=(a,a), r4=(0,a). There are no charges in the remaining lattice nodes.

For a given system of charges, it is necessary to determine the dipole moment and potential energy in an external electric field E = 0.1 V/m. To calculate the dipole moment, it is necessary to find the vector sum of the products of charges and the radius vector of each charge. Thus, the dipole moment of the system of charges is equal to: p = Q1 * r1 + Q2 * r2 + Q3 * r3 + Q4 * r4 = (-1kNl, 1kNl).

To calculate the potential energy of a system of charges in an external electric field E = 0.1 V/m, it is necessary to use the formula: P = Σ(Qi * φi), where Qi is the charge of each charge, and φi is the potential created by the charges. The potential φi at a point with coordinates r can be found by the formula: φi = k * Qi / |r - ri|, where k is the Coulomb constant, and ri is the radius vector of the i-th charge. Then the potential energy of the system of charges P is equal to:

P = k * (Q1 * φ1 + Q2 * φ2 + Q3 * φ3 + Q4 * φ4) = (9 * 10^9 N * m^2 / Cl^2) * [(1kNl) / |r| + (1nC) / |r - (a,0)| + (-1kNl) / |r - (a,a)| + (-1kNl) / |r - (0,a)|],

where |r|, |r - (a,0)|, |r - (a,a)| and |r - (0,a)| - distances between point r and charges Q1, Q2, Q3 and Q4, respectively.

Thus, this product provides a detailed solution to Problem 30305 to determine the dipole moment and potential energy of a system of charges located on a lattice. The description is given in html format, which allows you to conveniently read and study the material, as well as save and share information with others. Our store regularly updates and expands our range of digital products to provide customers with the most up-to-date information and the best user experience.

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Given a system of four point charges on a plane at lattice nodes with a cell in the shape of a square with side a=0.1 m:

Q1=1kNl, located at a node with radius vector r1=(0,0)

Q2=1nKl, located at a node with radius vector r2=(a,0)

Q3=-1kNl, located at a node with radius vector r3=(a,a)

Q4=-1kNl, located at a node with radius vector r4=(0,a)

To determine the dipole moment of a given system of charges, it is necessary to find the vector of the total charge and multiply it by the vector connecting the positive charge and the negative charge.

In this case, the total charge is zero, since the sum of the charges of the positive charges (Q1 and Q2) is equal to the sum of the charges of the negative charges (Q3 and Q4). Therefore, the dipole moment of the system is zero.

To determine the potential energy P of a system of charges, you must use the formula:

П = (1/2) * ∑(i=1 to N) ∑(j=i+1 to N) (qi*qj)/(4πε|r_i - r_j|),

where N is the number of charges in the system, qi and qj are the charges of the i-th and j-th charges, r_i and r_j are the radius vectors of the i-th and j-th charges, ε is the electric constant.

Substituting the values ​​of charges and radius vectors into this formula, we get:

P = (1/2) * [(Q1Q3)/(4πεa) + (Q1Q4)/(4πεa) + (Q2Q3)/(4πεa) + (Q2Q4)/(4πεa)]

Substituting the numerical values ​​of charges and constants, we get:

P = (1/2) * [(1kNl*(-1kNl))/(4π8.8510^(-12)0.1m) + (1kNl(-1kNl))/(4π8.8510^(-12)0.1m) + (1nCl(-1kNl))/(4π8.8510^(-12)0.1m) + (1nCl(-1kNl))/(4π8.8510^(-12)*0.1m)]

P = -3.60*10^(-8) J

Thus, the potential energy P of a system of charges in an external electric field E = 0.1 V/m is -3.60*10^(-8) J.

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