Q: Which of the following correctly expresses the magnitude of the cross product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

$$|\vec{A} \times \vec{B}| = |\vec{A}| |\vec{B}| \sin(\theta)$$

Q: A wire of length $$l$$ carrying current $$I is $$placed in a uniform magnetic field $$\vec{B}_{ext}. $$What is the formula for the magnetic force on the wire?

$$\vec{F} = I \vec{l} \times \vec{B}_{ext}$$

Q: A current loop with area $$A$$ and current $$I is $$placed in a uniform magnetic field $$\vec{B}. $$What is the expression for the torque on the loop?

$$\vec{\tau} = \vec{m} \times \vec{B}$$, where $$\vec{m} = I \vec{A}$$

Question 1

Which of the following correctly expresses the magnitude of the cross product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$|\vec{A} 	imes \vec{B}| = |\vec{A}| |\vec{B}| \sin(	heta)$$

Question 2

A charged particle moves with velocity $$\vec{v} in a $$uniform magnetic field $$\vec{B}. $$Under which condition will the magnetic force on the particle be zero?

Accepted Answer

When $$\vec{v} is $$parallel to $$\vec{B}$$

Question 3

The magnetic field at a distance $$r$$ from a very long straight wire carrying current $$I is $$given by which formula?

Accepted Answer

$$|\vec{B}| = \dfrac{\mu_0$ I}{2 \pi r}$$

Question 4

A circular current loop of radius $$a$$ carries current $$I. $$What is the magnetic field at a point on the axis of the loop, a distance $$x$$ from its center?

Accepted Answer

$$B = \dfrac{\mu_0$ I a^2$}{2 (x^2$ + a^2$)^{3/2}$$}$

Question 5

Inside an infinitely long solenoid with $$n$$ turns per unit length and current $$I$$, what is the magnitude of the magnetic field?

Accepted Answer

$$B = \mu_0$ n I$$

Question 6

A wire of length $$l$$ carrying current $$I is $$placed in a uniform magnetic field $$\vec{B}_{ext}. $$What is the formula for the magnetic force on the wire?

Accepted Answer

$$\vec{F} = I \vec{l} 	imes \vec{B}_{ext}$$

Question 7

A charged particle of mass $$m$$ and charge $$q$$ moves perpendicular to a uniform magnetic field $$B. $$What is the radius $$R of $$its circular path?

Accepted Answer

$$R = \dfrac{mv}{qB}$$

Question 8

Which statement about the direction of the cross product $$\vec{A} 	imes \vec{B} is $$correct?

Accepted Answer

It is perpendicular to both $$\vec{A}$$ and $$\vec{B}$$

Question 9

A current loop with area $$A$$ and current $$I is $$placed in a uniform magnetic field $$\vec{B}. $$What is the expression for the torque on the loop?

Accepted Answer

$$\vec{	au} = \vec{m} 	imes \vec{B}$$, where $$\vec{m} = I \vec{A}$$

Question 10

In a velocity selector, charged particles move undeflected when their speed $$v$$ satisfies which condition?

Accepted Answer

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

Question 11

A mass spectrometer separates ions according to their mass-to-charge ratio. If an ion of mass $$m$$ and charge $$q$$ moves in a magnetic field $$B$$ with radius $$R$$, what is the correct relationship?

Accepted Answer

$$\dfrac{m}{q} = \dfrac{B R}{v}$$

Question 12

Thomson's $$e/m$$ experiment showed that the $$e/m$$ ratio for electrons is independent of which of the following?

Accepted Answer

The cathode material

Question 13

A charged particle moves in a uniform magnetic field with velocity not perpendicular to the field. What is the resulting path?

Accepted Answer

Helical

Question 14

The SI unit of magnetic field is:

Accepted Answer

Tesla

Question 15

If a current-carrying wire is placed in a uniform magnetic field, under which condition will the wire experience zero magnetic force?

Accepted Answer

When the current is parallel to the magnetic field

Question 16

A charged particle of charge $$q$$ and mass $$m$$ moves in a uniform magnetic field $$B$$ with speed $$v. $$What is the cyclotron frequency $$\omega$$?

Accepted Answer

$$\omega = \dfrac{qB}{m}$$

Question 17

The magnetic potential energy $$U of a $$magnetic dipole moment $$\vec{m} in a $$magnetic field $$\vec{B} is $$given by:

Accepted Answer

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

Question 18

A proton moves in a uniform magnetic field $$\vec{B}$$ directed into the page. If its velocity $$\vec{v} is $$perpendicular to $$\vec{B}$$, what is the direction of the magnetic force acting on the proton?

Accepted Answer

Perpendicular to both $$\vec{v}$$ and $$\vec{B}$$, determined by the right-hand rule

Magnetic Fields and Magnetic Forces: Study Notes

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