Question 1

Consider a wire bent in the hairpin shape shown below. The wire carries a conventional current I as shown. What is the magnitude $|\vec{B}|$ of the magnetic field
-(a) at point a?

Accepted Answer

The magnetic field at point a due to a straight wire segment is given by $\mu_{0} I / 4 \pi R$ for each side of the hairpin. The semicircular part contributes an additional $\mu_{0} I / 2 R$. Adding these contributions together gives $(2+\pi) \mu_{0} I / 4 \pi R$.

Question 2

Consider a wire bent in the hairpin shape shown below. The wire carries a conventional current I as shown. What is the magnitude $|\vec{B}|$ of the magnetic field
-(b) at point $b$ ?

Accepted Answer

The answer of Consider a wire bent in the hairpin...

Question 3

Consider a metal bar moving through a uniform magnetic field, as shown below. (Assume that there is no electric field in this diagram's implied reference frame.)
  
Observers in all reference frames will agree (perhaps by tracking single electrons) that the bar's left side becomes negatively charged and its right end becomes positively charged, meaning that just after the bar begins to move (but before the charges have time to pile up at the ends) some leftward electromagnetic force must have been acting on the bar's electrons. What type of force is this
-(a) in the implied reference frame of the diagram above?

Accepted Answer

In the implied reference frame of a diagram that suggests motion of a bar in a magnetic field (though not visible here, it's a common physics scenario), the force on the bar's electrons is purely magnetic. This is due to the motion of the bar through a magnetic field, which induces a magnetic force on the electrons, following the right-hand rule for magnetic forces.

Question 4

Consider a metal bar moving through a uniform magnetic field, as shown below. (Assume that there is no electric field in this diagram's implied reference frame.)
  
Observers in all reference frames will agree (perhaps by tracking single electrons) that the bar's left side becomes negatively charged and its right end becomes positively charged, meaning that just after the bar begins to move (but before the charges have time to pile up at the ends) some leftward electromagnetic force must have been acting on the bar's electrons. What type of force is this
-(b) in the rest frame of the bar?

Accepted Answer

In the rest frame of the bar, the electrons are not moving relative to the bar, so there is no magnetic force acting on them. However, if there is a force acting on the electrons in another frame (such as a laboratory frame where the bar might be moving), this force must be accounted for by an electric field in the rest frame of the bar, leading to a purely electric force on the electrons.

Question 5

Consider the situation shown in problem E11T. 1 (before charges have time to pile up at the bar's ends).
 
-(a) There is an electric field in the bar's rest frame.

Accepted Answer

In the bar's rest frame, the bar is stationary and the charges are moving. This creates an electric field in the bar's rest frame.

Question 6

Consider the situation shown in problem E11T. 1 (before charges have time to pile up at the bar's ends).
 
-(b) There is a magnetic field in the bar's rest frame.

Accepted Answer

In the bar's rest frame, the bar is stationary and the charges within it are moving. According to the theory of special relativity, moving charges create a magnetic field. Therefore, there is a magnetic field in the bar's rest frame.

Question 7

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below.
  
Proton $\vec{v}$
First consider the frame in which the rod is at rest (the frame assumed in the diagram).
-(a) The rod creates an electric field in that frame.

Accepted Answer

In the frame where the rod is moving, it will appear to have a length contraction due to relativistic effects, altering the charge density and creating an electric field.

Question 8

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below.
  
Proton $\vec{v}$
First consider the frame in which the rod is at rest (the frame assumed in the diagram).
-(b) The rod creates a magnetic field in that frame.

Accepted Answer

The answer of Consider a proton moving parallel to a...

Question 9

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below.
  
Proton $\vec{v}$
First consider the frame in which the rod is at rest (the frame assumed in the diagram).
-(c) The proton feels an electric force in that frame.

Accepted Answer

In a frame where a charged particle like a proton is moving, it experiences an electric force due to its interaction with electric fields, as described by Coulomb's law.

Question 10

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below.
  
Proton $\vec{v}$
First consider the frame in which the rod is at rest (the frame assumed in the diagram).
-(d) The proton feels a magnetic force in that frame.

Accepted Answer

The answer of Consider a proton moving parallel to a...

Question 11

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below.
  
Proton $\vec{v}$
First consider the frame in which the rod is at rest (the frame assumed in the diagram).
-(e) The rod creates an electric field in that frame.

Accepted Answer

In the frame where the rod is moving, it will appear to have an electric field due to the relativistic effect of length contraction, which affects the distribution of charges and thus creates an electric field.

Question 12

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below.
  
Proton $\vec{v}$
First consider the frame in which the rod is at rest (the frame assumed in the diagram).
-(f) The rod creates a magnetic field in that frame.

Accepted Answer

When a charged rod moves, it creates a magnetic field due to the motion of its charges, as per the principles of electromagnetism.

Question 13

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below.
  
Proton $\vec{v}$
First consider the frame in which the rod is at rest (the frame assumed in the diagram).
-(g) The proton feels an electric force in that frame.

Accepted Answer

In any frame, a proton, which is a charged particle, will feel an electric force if it is in an electric field or if there are other charged particles present that can interact with it through electromagnetic forces.

Question 14

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below.
  
Proton $\vec{v}$
First consider the frame in which the rod is at rest (the frame assumed in the diagram).
-(h) The proton feels a magnetic force in that frame.

Accepted Answer

The answer of Consider a proton moving parallel to a...

Question 15

Imagine a source that in one inertial reference frame creates a uniform electric field but no magnetic field. In another inertial reference frame, the same source might create a magnetic field but no electric field.

Accepted Answer

According to the principles of electromagnetism, specifically the theory of relativity, if a source creates a uniform electric field in one inertial frame, it will create both electric and magnetic fields in another inertial frame moving relative to the first.

Question 16

If the electric and magnetic fields at a point are both zero in any given frame, they are zero in all frames.

Accepted Answer

The electric and magnetic fields are related by the Maxwell equations, which are Lorentz invariant. This means that the fields transform in the same way under a Lorentz transformation, so if they are zero in one frame, they are zero in all frames.

Question 17

Consider a magnetic field that (as shown in the diagram to the left below) points purely in the $-z$ direction in the unprimed frame (the $+z$ axis points toward the viewer in the drawing). There is zero electric field in this frame.
  
Consider a primed frame that moves in the $+x$ direction with respect to the unprimed frame. Choose from the answers above and to the right to indicate the direction of
-(a) the electric field in the primed frame.

Accepted Answer

The answer of Consider a magnetic field that (as shown...

Question 18

Consider a magnetic field that (as shown in the diagram to the left below) points purely in the $-z$ direction in the unprimed frame (the $+z$ axis points toward the viewer in the drawing). There is zero electric field in this frame.
  
Consider a primed frame that moves in the $+x$ direction with respect to the unprimed frame. Choose from the answers above and to the right to indicate the direction of
-(b) the magnetic field in the primed frame.

Accepted Answer

The answer of Consider a magnetic field that (as shown...

Question 19

Consider an electric field that (as shown in the diagram to the left below) points purely in the $-z$ direction in the unprimed frame (the $+z$ axis points toward the viewer in the drawing). There is zero magnetic field in this frame.
  
Consider a primed frame that moves in the $+x$ direction with respect to the unprimed frame. Choose from the answers above and to the right to indicate the direction of
-(a) the electric field in the primed frame.

Accepted Answer

The electric field in the primed frame is away from the viewer. This is because the magnetic field in the primed frame is in the positive y-direction, and the electric field is always perpendicular to the magnetic field.

Question 20

Consider an electric field that (as shown in the diagram to the left below) points purely in the $-z$ direction in the unprimed frame (the $+z$ axis points toward the viewer in the drawing). There is zero magnetic field in this frame.
  
Consider a primed frame that moves in the $+x$ direction with respect to the unprimed frame. Choose from the answers above and to the right to indicate the direction of
-the magnetic field in the primed frame.

Accepted Answer

The answer of Consider an electric field that (as shown...

Quiz 4: Electricity and Magnetism Are Unified

Consider a wire bent in the hairpin shape shown below. The wire carries a conventional current I as shown. What is the magnitude ∣B⃗∣|\vec{B}|∣B∣ of the magnetic field -(a) at point a?

Consider a wire bent in the hairpin shape shown below. The wire carries a conventional current I as shown. What is the magnitude ∣B⃗∣|\vec{B}|∣B∣ of the magnetic field -(b) at point bbb ?

Consider the situation shown in problem E11T. 1 (before charges have time to pile up at the bar's ends). -(a) There is an electric field in the bar's rest frame.

Consider the situation shown in problem E11T. 1 (before charges have time to pile up at the bar's ends). -(b) There is a magnetic field in the bar's rest frame.

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below. Proton v⃗\vec{v}v First consider the frame in which the rod is at rest (the frame assumed in the diagram). -(a) The rod creates an electric field in that frame.

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below. Proton v⃗\vec{v}v First consider the frame in which the rod is at rest (the frame assumed in the diagram). -(b) The rod creates a magnetic field in that frame.

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below. Proton v⃗\vec{v}v First consider the frame in which the rod is at rest (the frame assumed in the diagram). -(c) The proton feels an electric force in that frame.

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below. Proton v⃗\vec{v}v First consider the frame in which the rod is at rest (the frame assumed in the diagram). -(d) The proton feels a magnetic force in that frame.

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below. Proton v⃗\vec{v}v First consider the frame in which the rod is at rest (the frame assumed in the diagram). -(e) The rod creates an electric field in that frame.

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below. Proton v⃗\vec{v}v First consider the frame in which the rod is at rest (the frame assumed in the diagram). -(f) The rod creates a magnetic field in that frame.

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below. Proton v⃗\vec{v}v First consider the frame in which the rod is at rest (the frame assumed in the diagram). -(g) The proton feels an electric force in that frame.

Consider a proton moving parallel to a positively charged infinite thin rod at rest, as shown below. Proton v⃗\vec{v}v First consider the frame in which the rod is at rest (the frame assumed in the diagram). -(h) The proton feels a magnetic force in that frame.

Imagine a source that in one inertial reference frame creates a uniform electric field but no magnetic field. In another inertial reference frame, the same source might create a magnetic field but no electric field.

If the electric and magnetic fields at a point are both zero in any given frame, they are zero in all frames.

Consider a wire bent in the hairpin shape shown below. The wire carries a conventional current I as shown. What is the magnitude $|\vec{B}|$ of the magnetic field -(a) at point a?