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A smali, rigid object carries positive and negative 5.00 nc charges, It is oriented so that the positive charge has coordinates (−1.20 mm,1.00 mm) and the negative charge is at the point (1.30 mm,−1.30 mm ). (a) Find the electric dipole moment of the object.

User Envek
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Alright, let's first understand what an electric dipole moment is. The electric dipole moment for a pair of opposite charges of magnitude q is defined as the magnitude of the charge times the distance between them and the defined direction is from the negative to positive charge.

In the given case, we have a positive and negative charge both of 5.00 nC, and coordinates of the positive charge and negative charge are given as (-1.20 mm, 1.00 mm) and (1.30 mm, -1.30 mm) respectively. Here, note that 1nC = 1e-9C and 1mm = 1e-3m.

To calculate the electric dipole moment, we first have to calculate the displacement vector, which is the distance vector from the position of the negative charge to the position of the positive charge. This we can obtain by subtracting the position vector of the negative charge from the position vector of the positive charge.

The displacement vector would be:

displacement vector = positive_charge_coords - negative_charge_coords

Next, we calculate the magnitude of the dipole moment, which is given by the formula:

dipole_moment_magnitude = positive_charge * np.linalg.norm(displacement_vector)

The magnitude of the displacement vector is sqrt(x^2 + y^2), where x and y are the coordinates of the displacement vector.

Then we find the dipole moment vector which is the product of the charge and the displacement vector. The dipole moment vector would be:

dipole_moment_vector = positive_charge * displacement_vector

Upon solving the above steps and calculations, we get the electric dipole moment of the object as (1.6985287751463027e-11, array([-1.25e-11, 1.15e-11])).

This means that the magnitude of the electric dipole moment is 1.6985287751463027e-11, and it points in the direction specified by the vector [-1.25e-11, 1.15e-11].

User Zameer Manji
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