Question 1

A mass spectrometer is used to separate ions based on their mass-to-charge ratio. If an ion with charge $$q$$ and mass $$m$$ enters a region with a uniform magnetic field $$B$$ perpendicular to its velocity $$v$$, what is the radius $$r of $$its circular path?

Accepted Answer

$$r = \frac{mv}{qB}$$

Question 2

Which of the following best describes the difference between a magnetic dipole moment and an electric dipole moment?

Accepted Answer

A magnetic dipole moment arises from moving charges (currents), while an electric dipole moment arises from separated positive and negative charges.

Question 3

A current loop of area $$A$$ carries a current $$I. $$What is the magnitude of its magnetic dipole moment $$\mu$$?

Accepted Answer

$$\mu = I A$$

Question 4

A rectangular loop of wire with area $$A$$ and current $$I is $$placed in a uniform magnetic field $$B. $$The angle between the normal to the loop and the magnetic field is $$	heta. $$What is the expression for the torque $$	au on $$the loop?

Accepted Answer

$$	au = IAB \sin 	heta$$

Question 5

The energy $$U of a $$magnetic dipole moment $$\vec{\mu} in a $$uniform magnetic field $$\vec{B} is $$given by which of the following expressions?

Accepted Answer

$$U = -\vec{\mu} \cdot \vec{B}$$

Question 6

A circular loop of wire with radius $$r$$ carries a current $$I$$ and is placed in a uniform magnetic field $$B. If $$the plane of the loop is perpendicular to $$\vec{B}$$, what is the torque on the loop?

Accepted Answer

Zero

Question 7

A mass spectrometer is used to analyze a sample containing two isotopes of the same element. Both isotopes are singly ionized and enter the magnetic field with the same velocity. Which statement is correct about their paths?

Accepted Answer

The isotope with greater mass will have a larger radius of curvature.

Question 8

A current loop experiences a torque in a uniform magnetic field. What is the physical reason for this torque?

Accepted Answer

The forces on opposite sides of the loop are equal in magnitude but opposite in direction, creating a couple.

Question 9

If a current loop is oriented so that its magnetic dipole moment $$\vec{\mu} is $$anti-parallel to the external magnetic field $$\vec{B}$$, what is the potential energy of the system?

Accepted Answer

$$U = +\mu B$$

Question 10

A rectangular loop of wire is placed in a uniform magnetic field. The plane of the loop is initially parallel to the field. If the loop is rotated by $$90^\circ$$, what happens to the torque acting on it?

Accepted Answer

The torque increases from zero to a maximum value.

Question 11

A proton enters a mass spectrometer with velocity $$v$$ perpendicular to a magnetic field $$B. If $$the magnetic field is doubled, what happens to the radius of the proton's path?

Accepted Answer

It is halved.

Question 12

A current loop in a uniform magnetic field experiences a torque but no net force. Why?

Accepted Answer

The forces on opposite sides of the loop cancel each other out.

Question 13

A square loop of side $$l$$ carries a current $$I$$ and is placed in a uniform magnetic field $$B. $$What is the maximum torque experienced by the loop?

Accepted Answer

$$I l^2$ B$$

Question 14

A mass spectrometer is used in a hospital to identify isotopes in a blood sample. If the sample contains ions with the same charge but different masses, how does the spectrometer distinguish between them?

Accepted Answer

By measuring the different radii of curvature of their paths in the magnetic field.

Question 15

A current loop is placed in a uniform magnetic field. If the loop is free to rotate, what orientation will it eventually reach?

Accepted Answer

Its magnetic dipole moment will align parallel to the magnetic field.

Question 16

A circular loop of wire with area $$A$$ and current $$I is $$placed in a uniform magnetic field $$B. If $$the angle between the normal to the loop and the field is $$30^\circ$$, what is the torque on the loop?

Accepted Answer

$$IAB \sin 30^\circ$$

Question 17

A mass spectrometer is used to analyze a mixture of ions. If the velocity selector uses both electric and magnetic fields, what is the condition for an ion to pass through undeflected?

Accepted Answer

$$v = \frac{E}{B}$$

Question 18

A current loop is spinning about its vertical axis of symmetry in a uniform magnetic field. If the current is counterclockwise as seen from above and the magnetic force points into the plane of the loop, what is the direction of the external magnetic field?

Accepted Answer

The field is directed from above the loop into the plane (downward).

Magnetism: Mass Spectrometer, Magnetic Dipole Moments, and Magnetic Torque

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