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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?

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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.

This problem has been solved

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