Question 1

A 0.70-m radius cylindrical region contains a uniform electric field that is parallel to the axis and is increasing at the rate 5.0 * 10¹² V/m.s.The magnetic field at a point 0.25 m from the axis has a magnitude of:

Accepted Answer

The magnetic field can be calculated using Ampère's law with Maxwell's addition, which relates the change in electric field to the magnetic field. The formula is B = (μ₀ε₀r/2) * (dE/dt), where r is the distance from the axis. Substituting the given values, B = (4π x 10⁻⁷ T·m/A)(8.85 x 10⁻¹² C²/N·m²)(0.25 m/2) * (5.0 x 10¹² V/m·s) = 7.0 x 10⁻⁶ T.

Question 2

A cylindrical region contains a uniform electric field that is along the cylinder axis and is changing with time.If r is the distance from the cylinder axis the magnitude of the magnetic field within the region is:

Accepted Answer

According to Faraday's Law of Induction, a changing electric field produces a magnetic field. As the electric field is changing with time, it will produce a magnetic field. As the magnetic field is along the cylinder axis, its magnitude will be proportional to the perpendicular distance from the axis, i.e., r. Therefore, option E, proportional to r, is the correct choice.

Question 3

An electron is on the z axis moving toward the xy plane but it has not reached that plane yet.At that instant:

Accepted Answer

At the moment the electron has not reached the xy plane yet, there is no actual flow of charge through that plane, so there is no true current. However, according to Ampere's law, a changing electric field can induce a magnetic field, which induces a changing magnetic flux through a surface. This changing magnetic flux, in turn, can induce an electric field through the surface. This is known as displacement current. Therefore, there is only a displacement current through the xy plane.

Question 4

One of the Maxwell equations begins with  ....The symbol  means:

Accepted Answer

The symbol provided is a hexadecimal representation of a unique identifier (UUID). It does not correspond to any physical quantity or concept related to the Maxwell equations.

Question 5

One of the Maxwell equations begins with ....The ^o symbol in the integral sign means:

Accepted Answer

The ^o symbol in the integral sign represents integrating around a closed path.

Question 6

Gauss' law for magnetism:

Accepted Answer

The answer of Gauss' law for magnetism:
...

Question 7

Suppose you are looking into one end of a long cylindrical tube in which there is a uniform electric field, pointing away from you.If the magnitude of the field is decreasing with time the field lines of the induced magnetic field are:

Accepted Answer

The induced magnetic field lines form circles around the axis of the changing electric field, according to Ampère's law with Maxwell's addition. This is because a changing electric field induces a magnetic field, which, in this scenario, would be circular to conserve the angular symmetry of the system.

Question 8

The diagram shows one plate of a parallel-plate capacitor from within the capacitor.The plate is circular and has radius R.The dashed circles are four integration paths have radii of r₁ = R/4, r₂ = R/2, r₃ =3 R/2, and r₄ = 2R.Rank the paths according to the magnitude of around the paths during the discharging of the capacitor, least to greatest.

Accepted Answer

The answer of The diagram shows one plate of a...

Question 9

A cylindrical region contains a uniform electric field that is parallel to the axis and is changing with time.If r is the distance from the cylinder axis the magnitude of the magnetic field outside the region is:

Accepted Answer

According to Faraday's law of electromagnetic induction, a changing electric field induces a magnetic field. Outside the cylindrical region, the magnetic field is inversely proportional to the distance from the axis, hence proportional to 1/r.

Question 10

A 0.70-m radius cylindrical region contains a uniform electric field that is parallel to the axis and is increasing at the rate 5.0 *10¹² V/m.s.The magnetic field at a point 1.2 m from the axis has a magnitude of:

Accepted Answer

The magnetic field at a distance from the axis of a cylindrical region with a changing electric field can be found using Ampère's law with Maxwell's addition. The displacement current density is proportional to the rate of change of the electric field. For a point outside the cylindrical region, the magnetic field is determined by the total displacement current through the cross-sectional area of the cylinder. Using the given rate of change of the electric field and the radius of the cylinder, the magnetic field at 1.2 m from the axis is calculated to be approximately 1.1 x 10^-5 T.

Question 11

Suppose you are looking into one end of a long cylindrical tube in which there is a uniform electric field, pointing away from you.If the magnitude of the field is decreasing with time the direction of the induced magnetic field is:

Accepted Answer

According to Faraday's law of induction, a changing magnetic field induces an electric field, and a changing electric field induces a magnetic field. In this case, the decreasing electric field is changing with time, so it will induce a magnetic field. The direction of the induced magnetic field can be determined using Lenz's law, which states that the induced magnetic field opposes the direction of the change in the electric field that caused it. Since the electric field is decreasing away from you, the induced magnetic field will be in the direction that opposes this change, which is in the clockwise direction when viewed from your end of the tube.

Question 12

A magnetic field exists between the plates of a capacitor:

Accepted Answer

A magnetic field is created whenever there is a changing electric field, such as when a capacitor is being charged or discharged. Therefore, there is a magnetic field between the plates of a capacitor while it is being charged.

Question 13

A sinusoidal emf is connected to a parallel plate capacitor.The magnetic field between the plates is:

Accepted Answer

The magnetic field between the plates of a capacitor connected to a sinusoidal emf is sinusoidal and its amplitude is proportional to the frequency of the source due to the displacement current, which depends on the rate of change of the electric field.

Question 14

The statement that magnetic field lines form closed loops is a direct consequence of:

Accepted Answer

Gauss' law for magnetism states that the net magnetic flux out of any closed surface is zero, implying that magnetic field lines must form closed loops since they have neither beginning nor end points.

Question 15

A 1-A current is used to charge a parallel plate capacitor.A large square piece of paper is placed between the plates and parallel to them so it sticks out on all sides.The value of the integral  around the perimeter of the paper is:

Accepted Answer

The answer of A 1-A current is used to charge...

Question 16

According to Gauss' law for magnetism, magnetic field lines:

Accepted Answer

Gauss' law for magnetism states that magnetic field lines form closed loops, so the correct choice is A.

Question 17

A magnetic field parallel to the x axis with a magnitude that decreases with increasing x but does not change with y and z is impossible according to:

Accepted Answer

Gauss' law for magnetism states that the net magnetic flux through a closed surface is zero, implying that magnetic field lines must form closed loops. A magnetic field that decreases with increasing x without changing in y and z would imply a divergence in the field, violating this law.

Question 18

Gauss' law for magnetism,  , tells us:

Accepted Answer

Gauss' law for magnetism states that magnetic monopoles do not exist, which is the only correct statement among the given options. The other options either pertain to Gauss' law for electric fields or are unrelated to Gauss' law.

Question 19

An electric field exists in the cylindrical region shown and is parallel to the cylinder axis.The magnitude of the field might vary with time according to any of the four graphs shown.Rank the four variations according to the magnitudes of the magnetic field induced at the edge of the region, least to greatest.

Accepted Answer

The answer of An electric field exists in the cylindrical...

Question 20

Four closed surfaces are shown, each with circular top and bottom faces and curved sides.The areas A_top and A_bot of the top and bottom faces and the magnitudes B_top and B_bot of the uniform magnetic fields through the top and bottom faces are given.The fields are perpendicular to the faces and are either inward or outward.Rank the surfaces according to the magnitude of the magnetic flux through the curved sides, least to greatest.

Accepted Answer

The answer of Four closed surfaces are shown, each with...

Quiz 32: Maxwells Equations; Magnetism of Matter

A 0.70-m radius cylindrical region contains a uniform electric field that is parallel to the axis and is increasing at the rate 5.0 * 1012 V/m.s.The magnetic field at a point 0.25 m from the axis has a magnitude of: