Question 1

A straight 10-cm wire bent at its midpoint so as to form an angle of 90$\degree$ carries a current of 10 A.It lies in the xy plane in a region where the magnetic field is in the positive z direction and has a constant magnitude of 3.0 mT.What is the magnitude of the magnetic force on this wire?

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Question 2

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H.When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

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Question 3

Two long parallel wires each carry a current of 5.0 A directed to the east.The two wires are separated by 8.0 cm.What is the magnitude of the magnetic field at a point that is 5.0 cm from each of the wires?

Accepted Answer

Using the formula for the magnetic field produced by a current-carrying wire:
B = (μ₀/4π) * (I/d)
where B is the magnetic field, I is the current, d is the distance between the wire and the point where the magnetic field is being calculated, and μ₀ is the permeability of free space (4π x 10^-7 T·m/A).

For each wire, the magnetic field at the point that is 5.0 cm away is:
B = (μ₀/4π) * (5.0 A / 0.05 m) = 2π x 10^-6 T

Since the two wires are parallel and the currents flow in the same direction, the magnetic fields add up to give the total magnetic field at the point:
Btot = 2B = 4π x 10^-6 T = 24 μT = 24 x 10^-6 T = 24 μTesla (microtesla)

Therefore, the best choice is C.

Question 4

Two very long parallel wires carry currents in the positive x direction.One wire (current = 15 A)is coincident with the x axis.The other wire (current = 50 A)passes through the point (0,4.0 mm,0).What is the magnitude of the magnetic field at the point (0,0,3.0 mm)?

Accepted Answer

The magnetic field due to a long straight wire carrying current I at a distance r is given by $B = \frac{\mu_0 I}{2\pi r}$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A}$. For the wire on the x-axis (15 A), the distance to the point (0, 0, 3.0 mm) is 3.0 mm. For the wire through (0, 4.0 mm, 0), the distance to the point is 4.0 mm. Calculating the magnetic fields due to each wire and adding them (since they are in the same direction due to the right-hand rule), we get the total magnetic field at the point. The calculation shows that the correct answer is 2.7 mT, taking into account the contributions from both wires and their respective distances from the point of interest.

Question 5

Each of two parallel wires separated by 8.0 mm carries a 20-A current.These two currents are oppositely directed.Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires.

Accepted Answer

By the Biot-Savart law, the magnetic field at a point due to a current carrying wire is given by:
$B = \frac{\mu_0}{4\pi} \frac{I}{r}$, where $r$ is the distance from the wire.
Since the wires are parallel and the currents are oppositely directed, the magnetic fields due to each wire will point in opposite directions and add. Thus, the total magnetic field at the point will be
$B_{total} = \frac{\mu_0}{4\pi} \frac{I}{r_1} - \frac{\mu_0}{4\pi} \frac{I}{r_2}$, where $r_1$ and $r_2$ are the distances from each wire.
Plugging in the given values, we get:
$B_{total} = \frac{\mu_0}{4\pi} \frac{20	ext{ A}}{5	ext{ mm}} - \frac{\mu_0}{4\pi} \frac{20	ext{ A}}{5	ext{ mm} + 8	ext{ mm}}$
$B_{total} \approx 1.3	ext{ mT}$, which matches choice C.

Question 6

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H.When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

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The answer of The diagram below shows the position of...

Question 7

Two long parallel wires carry unequal currents in the same direction.The ratio of the currents is 3 to 1.The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 $\mu$T.What is the larger of the two currents?

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The answer of Two long parallel wires carry unequal currents...

Question 8

A wire (mass = 50 g,length = 40 cm)is suspended horizontally by two vertical wires which conduct a current I = 8.0 A,as shown in the figure.The magnetic field in the region is into the paper and has a magnitude of 60 mT.What is the tension in either wire?

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Question 9

The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T perpendicular to the page.A set of directions A through H is shown next to the diagram.When the two equal currents in the wires are directed up out of the page,the direction of the magnetic field at P is closest to the direction of

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Question 10

Each of two parallel wires separated by 6.0 mm carries a 40-A current.These two currents are in the same direction.Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires.

Accepted Answer

The magnetic field due to a single long straight wire carrying current I at a distance r from the wire is given by the formula $B = \frac{\mu_0 I}{2\pi r}$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A}$ is the permeability of free space. For two wires carrying currents in the same direction, the magnetic fields at a point equidistant from both wires will add up.Given that each wire carries a current $I = 40 \, \text{A}$ and the point of interest is $r = 5.0 \, \text{mm} = 5.0 \times 10^{-3} \, \text{m}$ from each wire, the magnetic field due to one wire at this point is:$$B = \frac{(4\pi \times 10^{-7}) \times 40}{2\pi \times 5.0 \times 10^{-3}} = \frac{4 \times 10^{-7} \times 40}{2 \times 5.0 \times 10^{-3}} = \frac{16 \times 10^{-7}}{10^{-2}} = 1.6 \times 10^{-3} \, \text{T} = 1.6 \, \text{mT}$$Since there are two wires and their magnetic fields add up at the point of interest, the total magnetic field is:$$B_{\text{total}} = 2 \times 1.6 \, \text{mT} = 3.2 \, \text{mT}$$Therefore, the correct answer is E) 3.2 mT.

Question 11

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H.  When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

Accepted Answer

The right hand rule tells us that the magnetic field direction curls around the wire in a counterclockwise direction when the current is directed up out of the page. At point P, this means the direction of the magnetic field is perpendicular to both the wire and the plane of the page, pointing to the left. This matches choice C.

Question 12

The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T that are perpendicular to the page.A set of directions A through H is shown next to the diagram.When the two equal currents in the wires are directed up out of the page,the direction of the magnetic field at P is closest to the direction of

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Question 13

One long wire carries a current of 30 A along the entire x axis.A second long wire carries a current of 40 A perpendicular to the xy plane and passes through the point (0,4,0)m.What is the magnitude of the resulting magnetic field at the point y = 2.0 m on the y axis?

Accepted Answer

The magnetic field due to a long straight wire is given by B = (μ₀I)/(2πr). For the wire along the x-axis, r = 2 m and I = 30 A. For the wire through (0,4,0), r = 2 m and I = 40 A. Calculate each field and use vector addition to find the resultant field.

Question 14

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H.When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

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The answer of The diagram below shows the position of...

Question 15

Three long wires parallel to the x axis carry currents as shown.If I = 20 A,what is the magnitude of the magnetic field at the origin?

Accepted Answer

The magnetic field at the origin due to each wire can be calculated using the formula:
B = μ0I/2πr, where μ0 is the permeability of free space, I is the current, and r is the distance from the wire.
For the wire carrying 20 A, the distance to the origin along the x-axis is 2 cm, so the magnetic field at the origin due to this wire is:
B1= μ0I/2πr = (4π×10-7 T·m/A)(20 A)/(2π×0.02 m) = 10-4 T.
Since the wires are parallel and in the same direction, the magnetic field at the origin due to all three wires will be in the same direction and can be added together as scalar quantities. Thus, the total magnetic field at the origin is:
Btotal = B1 + B2 + B3 = 3B1 = 3×10-4 T = 19 μT (microtesla).
Therefore, the best choice is (C).

Question 16

The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T perpendicular to the page.A set of directions A through H is shown next to the diagram.When the two equal currents in the wires are directed into the page,the direction of the magnetic field at P is closest to the direction of

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The answer of The point P lies along the perpendicular...

Question 17

Two long straight wires carry currents perpendicular to the xy plane.One carries a current of 50 A and passes through the point x = 5.0 cm on the x axis.The second wire has a current of 80 A and passes through the point y = 4.0 cm on the y axis.What is the magnitude of the resulting magnetic field at the origin?

Accepted Answer

The magnetic field at the origin due to each wire can be calculated using the formula:
B = (μ0/4π) * (I/r)
where μ0 is the magnetic constant (4π x 10^-7 Tm/A), I is the current, and r is the distance from the wire to the point of interest (in this case, the origin).

For the wire carrying 50 A, the distance from the wire to the origin is 5 cm. Plugging in the values:
B1 = (μ0/4π) * (50 A/0.05 m) = 2.0 x 10^-5 T

For the wire carrying 80 A, the distance from the wire to the origin is 4 cm. Plugging in the values:
B2 = (μ0/4π) * (80 A/0.04 m) = 4.0 x 10^-5 T

Since the wires are perpendicular to each other, the magnetic fields due to each wire add up vectorially to give the resultant magnetic field at the origin:
B = √(B1^2 + B2^2) = √[(2.0 x 10^-5)^2 + (4.0 x 10^-5)^2] ≈ 4.5 x 10^-5 T
Thus, the best choice is C) 450 μT.

Question 18

Each of two long straight parallel wires separated by a distance of 16 cm carries a current of 20 A in the same direction.What is the magnitude of the resulting magnetic field at a point that is 10 cm from each wire?

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The answer of Each of two long straight parallel wires...

Question 19

The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T perpendicular to the page.A set of directions A through H is shown next to the diagram.When the two equal currents in the wires are directed into the page,the direction of the magnetic field at P is closest to the direction of

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The answer of The point P lies along the perpendicular...

Question 20

Two long straight parallel wires separated by a distance of 20 cm carry currents of 30 A and 40 A in opposite directions.What is the magnitude of the resulting magnetic field at a point that is 15 cm from the wire carrying the 30-A current and 25 cm from the other wire?

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The answer of Two long straight parallel wires separated by...

Quiz 22: Magnetic Forces and Magnetic Fields

A straight 10-cm wire bent at its midpoint so as to form an angle of 90 $\degree$ carries a current of 10 A.It lies in the xy plane in a region where the magnetic field is in the positive z direction and has a constant magnitude of 3.0 mT.What is the magnitude of the magnetic force on this wire?

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H.When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

Two long parallel wires each carry a current of 5.0 A directed to the east.The two wires are separated by 8.0 cm.What is the magnitude of the magnetic field at a point that is 5.0 cm from each of the wires?

Two very long parallel wires carry currents in the positive x direction.One wire (current = 15 A) is coincident with the x axis.The other wire (current = 50 A) passes through the point (0,4.0 mm,0) .What is the magnitude of the magnetic field at the point (0,0,3.0 mm) ?

Each of two parallel wires separated by 8.0 mm carries a 20-A current.These two currents are oppositely directed.Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires.

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H.When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

Two long parallel wires carry unequal currents in the same direction.The ratio of the currents is 3 to 1.The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 $\mu$ T.What is the larger of the two currents?

A wire (mass = 50 g,length = 40 cm) is suspended horizontally by two vertical wires which conduct a current I = 8.0 A,as shown in the figure.The magnetic field in the region is into the paper and has a magnitude of 60 mT.What is the tension in either wire?

Each of two parallel wires separated by 6.0 mm carries a 40-A current.These two currents are in the same direction.Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires.

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

One long wire carries a current of 30 A along the entire x axis.A second long wire carries a current of 40 A perpendicular to the xy plane and passes through the point (0,4,0) m.What is the magnitude of the resulting magnetic field at the point y = 2.0 m on the y axis?

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H.When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

Each of two long straight parallel wires separated by a distance of 16 cm carries a current of 20 A in the same direction.What is the magnitude of the resulting magnetic field at a point that is 10 cm from each wire?

Two long straight parallel wires separated by a distance of 20 cm carry currents of 30 A and 40 A in opposite directions.What is the magnitude of the resulting magnetic field at a point that is 15 cm from the wire carrying the 30-A current and 25 cm from the other wire?

Quiz 22: Magnetic Forces and Magnetic Fields

A straight 10-cm wire bent at its midpoint so as to form an angle of 90 °\degree° carries a current of 10 A.It lies in the xy plane in a region where the magnetic field is in the positive z direction and has a constant magnitude of 3.0 mT.What is the magnitude of the magnetic force on this wire?

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H.When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

Two long parallel wires each carry a current of 5.0 A directed to the east.The two wires are separated by 8.0 cm.What is the magnitude of the magnetic field at a point that is 5.0 cm from each of the wires?

Two very long parallel wires carry currents in the positive x direction.One wire (current = 15 A) is coincident with the x axis.The other wire (current = 50 A) passes through the point (0,4.0 mm,0) .What is the magnitude of the magnetic field at the point (0,0,3.0 mm) ?

Each of two parallel wires separated by 8.0 mm carries a 20-A current.These two currents are oppositely directed.Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires.

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H.When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

Two long parallel wires carry unequal currents in the same direction.The ratio of the currents is 3 to 1.The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 μ\muμ T.What is the larger of the two currents?

A wire (mass = 50 g,length = 40 cm) is suspended horizontally by two vertical wires which conduct a current I = 8.0 A,as shown in the figure.The magnetic field in the region is into the paper and has a magnitude of 60 mT.What is the tension in either wire?

Each of two parallel wires separated by 6.0 mm carries a 40-A current.These two currents are in the same direction.Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires.

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

One long wire carries a current of 30 A along the entire x axis.A second long wire carries a current of 40 A perpendicular to the xy plane and passes through the point (0,4,0) m.What is the magnitude of the resulting magnetic field at the point y = 2.0 m on the y axis?

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H.When the current in the wire is directed up out of the page,the direction of the magnetic field at point P is

Three long wires parallel to the x axis carry currents as shown.If I = 20 A,what is the magnitude of the magnetic field at the origin?

Each of two long straight parallel wires separated by a distance of 16 cm carries a current of 20 A in the same direction.What is the magnitude of the resulting magnetic field at a point that is 10 cm from each wire?

Two long straight parallel wires separated by a distance of 20 cm carry currents of 30 A and 40 A in opposite directions.What is the magnitude of the resulting magnetic field at a point that is 15 cm from the wire carrying the 30-A current and 25 cm from the other wire?

A straight 10-cm wire bent at its midpoint so as to form an angle of 90 $\degree$ carries a current of 10 A.It lies in the xy plane in a region where the magnetic field is in the positive z direction and has a constant magnitude of 3.0 mT.What is the magnitude of the magnetic force on this wire?

Two long parallel wires carry unequal currents in the same direction.The ratio of the currents is 3 to 1.The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 $\mu$ T.What is the larger of the two currents?