Question

An electric dipole with charges is centered at the origin in the xy-plane and oriented with its electric dipole moment along the negative y-direction. The charge separation is 6 mm. What is the electric field due to this dipole at the point 0.00 m and -12.0 m

Answer 1

The electric field due to a dipole can be calculated using the formula E = (1 / (4πε₀)) * (2p / r³), where E is the electric field, ε₀ is the vacuum permittivity, p is the electric dipole moment, and r is the distance from the dipole.

Step-by-step explanation:

The electric field due to a dipole can be calculated using the formula:

E = (1 / (4πε₀)) * (2p / r³)

where E is the electric field, ε₀ is the vacuum permittivity, p is the electric dipole moment, and r is the distance from the dipole. In this case, the dipole moment is along the negative y-direction.

Using the given information, the charge separation is 6 mm, which can be converted to meters as 0.006 m. The distance from the dipole to the point (0.00 m, -12.0 m) is 12.0 m. Plugging these values into the formula:

E = (1 / (4πε₀)) * (2p / r³)

E = (1 / (4πε₀)) * (2(-q)(0.006) / (12.0)³)

where -q represents the magnitude of the charge. Solving for E will give us the electric field at the given point.

Answer 2

The electric field at a point on the axis of a dipole is given by the formula E = (1/(4πε_0)) * (2μ/r^3), where μ is the dipole moment and r is the distance from the dipole. The actual calculation requires knowledge of the charge amount and the permittivity of free space.

Step-by-step explanation:

To determine the electric field due to an electric dipole at a specific point, we need to consider the dipole moment and the positions of the charges. The dipole moment μ is defined as the product of the charge q and the separation distance d, and it points from the negative to the positive charge. In this scenario, we're dealing with a point along the y-axis, below the dipole. The electric field due to a dipole at a point along the axial line (i.e., the line which extends in the dipole's direction) is given by

E = (1/(4πε0)) * (2μ/r3)

where ε0 is the vacuum permittivity, and r is the distance from the center of the dipole to the point of interest. However, this formula assumes that the point is far from the dipole compared to the separation of the charges (r >> d). If this is not the case, the exact expression for the field should be used, calculating contributions from each charge individually.