Consider an electric dipole on the x-axis and centered at the origin. At a distance h = 18.9 cm along the positive x-axis, the magnitude of electric field due to the electric dipole is given by k(2qd)h3𝑘(2𝑞𝑑)ℎ3 , where q = 3.07 μC and d = 2.57 cm. Find a distance perpendicular to the x-axis and measured from the origin at which the magnitude of the electric field is the same. (You may enter your calculation using scientific notation.) m
Question
Consider an electric dipole on the x-axis and centered at the origin. At a distance h = 18.9 cm along the positive x-axis, the magnitude of electric field due to the electric dipole is given by k(2qd)h3𝑘(2𝑞𝑑)ℎ3 , where q = 3.07 μC and d = 2.57 cm. Find a distance perpendicular to the x-axis and measured from the origin at which the magnitude of the electric field is the same. (You may enter your calculation using scientific notation.) m
Solution
The electric field due to a dipole at a point on the axial line is given by E = k(2qd)/h^3, where q is the charge, d is the distance between the charges, h is the distance from the center of the dipole, and k is Coulomb's constant.
The electric field due to a dipole at a point on the equatorial line (perpendicular to the axis) is given by E = k(qd)/r^3, where r is the distance from the center of the dipole.
We are given that the electric field at a point on the axial line is the same as the electric field at a point on the equatorial line. Therefore, we can equate the two expressions and solve for r:
k(2qd)/h^3 = k(qd)/r^3
Solving for r, we get:
r = ((2qd)/h^3)^(1/3)
Substituting the given values:
r = ((2 * 3.07 * 10^-6 C * 2.57 * 10^-2 m) / (18.9 * 10^-2 m)^3)^(1/3)
After calculating the above expression, we get the distance r.
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