A water molecule has a permanent dipole moment of 6.20×10-30 Cm, and if you put one in an electric field it will feel a torque and try to rotate (this is essentially how a microwave oven works, although that electric field oscillates). What is the torque on the molecule if its dipole moment is oriented at 27.9° with respect to the electric field, which has a strength of 2.95×104 N/C?
Question
A water molecule has a permanent dipole moment of 6.20×10-30 Cm, and if you put one in an electric field it will feel a torque and try to rotate (this is essentially how a microwave oven works, although that electric field oscillates). What is the torque on the molecule if its dipole moment is oriented at 27.9° with respect to the electric field, which has a strength of 2.95×104 N/C?
Solution
The torque τ experienced by a dipole in a uniform electric field is given by the equation:
τ = pEsinθ
where: p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the electric field.
Given: p = 6.20×10^-30 Cm, E = 2.95×10^4 N/C, and θ = 27.9°.
First, convert the angle from degrees to radians because the trigonometric functions in calculators use radians.
θ = 27.9° * (π rad / 180°) = 0.487 rad
Then, substitute the given values into the equation:
τ = (6.20×10^-30 Cm) * (2.95×10^4 N/C) * sin(0.487 rad)
Calculate the above expression to find the torque.
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