To use a larger sample, the experimenters construct a...

To use a larger sample, the experimenters construct a solenoid that has the same length, type of wire, and loop spacing but twice the diameter of the original. How does the maximum possible magnetic torque on a bacterium in this new solenoid compare with the torque the bacterium would have experienced in the original solenoid? Assume that the currents in the solenoids are the same. The maximum torque in the new solenoid is (a) twice that in the original one; (b) half that in the original one; (c) the same as that in the original one; (d) one-quarter that in the original one.

Key Concepts

Magnetic Field in a Solenoid

The magnetic field inside a solenoid is determined primarily by the current and the number of turns per unit length, rather than by the physical diameter of the solenoid. When the current and turn spacing remain constant, the internal magnetic field does not change even if the solenoid's diameter is altered.

Magnetic Dipole Torque

A magnetic dipole in an external magnetic field experiences a torque that is proportional to the product of the dipole's magnetic moment and the field strength, expressed as ? = mB sin?. The maximum torque occurs when the dipole is oriented perpendicular to the field, and if the magnetic field remains constant, the maximum torque will also remain unchanged.

Geometry and Magnetic Field Uniformity

Altering the geometric dimensions of a solenoid, such as doubling its diameter while maintaining the same current and loop spacing, has no impact on the internal magnetic field strength. The uniformity and magnitude of the field are preserved, meaning that devices relying on that field, like a torque-experiencing bacterium, will experience the same magnetic conditions regardless of the solenoid’s diameter.

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