What is the dipole moment vector, in component form, for the connected charges?

Question

What is the dipole moment vector, in component form, for the connected charges? Express the component vectors using the specified x- and y- coordinates. Calculate the torque vector exerted on this dipole due to a constant electric field of magnitude, Ereplace 1000 N/C. The direction of the electric field is fixed and oriented at an angle, theta2replace 15degree, below the horizontal direction, as shown. What is the electric potential energy associated with this dipole and electric field? Assuming the electric dipole is fixed at the midpoint between the charges and can rotate freely in the electric field, calculate the angular frequency (omega) for the oscillation of the dipole?

Explanation / Answer

i.the dipole moment vector in component form is px= 2d * q * cos1 and py= 2d * q * sin1 q = 0.01 C and 1 = 10o substitute the values ii.the torque vector exerted on the dipole is = 2dq * E * sin2 E = 1000 N/C and 2= 15o iii)the electric potential energy associated with this dipoleand electric field is U = -p * E * cos2 = -2dq * E * cos2 iv)the kinetic energy of the charge is (1/2)m * v^2 = U or v = (2U/m)^(1/2) m = 9.1 * 10^-31 kg We know that v = (d/2) * w or w = (2v/d) iii)the electric potential energy associated with this dipoleand electric field is U = -p * E * cos2 = -2dq * E * cos2 iv)the kinetic energy of the charge is (1/2)m * v^2 = U or v = (2U/m)^(1/2) m = 9.1 * 10^-31 kg We know that v = (d/2) * w or w = (2v/d)

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