Question 1

A 198-m-long wire carrying a current of 3.5 A will be accompanied by a magnetic field of what strength at a distance of 0.054 m from the wire? (magnetic permeability in empty space µ₀ = 4π × 10−⁷ T⋅m/A)

Accepted Answer

The magnetic field produced by a current-carrying wire at a distance r is given by the formula:

B = μ₀I/(2πr)

where B is the magnetic field, I is the current, r is the distance, and μ₀ is the magnetic permeability in empty space.

Substituting the given values, we get:

B = (4π × 10−7 T⋅m/A) × 3.5 A /(2π × 0.054 m)

= 1.3 × 10−5 T

Therefore, the magnetic field at a distance of 0.054 m from the wire is 1.3 × 10−5 T.
The correct choice is C.

Question 2

An incredible amount of electrical energy passes down the funnel of a large tornado every second.Measurements at a distance of 12.8 km from a large tornado showed an almost constant magnetic field of 2.35 × 10−⁸ T associated with the tornado.What was the average current going down the funnel? (µ₀ = 4π × 10−⁷ T⋅m/A)

Accepted Answer

The answer of An incredible amount of electrical energy passes...

Question 3

A superconducting wire carries a current of 7.0 kA.Find the magnetic field at a distance of 1.5 m from the wire.(µ₀ = 4π × 10−⁷ T⋅m/A)

Accepted Answer

The magnetic field at a distance $r$ from a long straight wire carrying a current $I$ is given by the formula $B = \frac{\mu_0 I}{2\pi r}$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}$, $I = 7.0 \, \text{kA} = 7000 \, \text{A}$, and $r = 1.5 \, \text{m}$. Plugging these values into the formula gives $B = \frac{4\pi \times 10^{-7} \times 7000}{2\pi \times 1.5} = 9.3 \times 10^{-4} \, \text{T}$, which corresponds to choice A.

Question 4

Two long parallel wires 10.0 cm apart carry currents of 3.0 A and 2.9 A in the same direction.Is there any point between the two wires where the magnetic field is zero?

Accepted Answer

The magnetic field created by a current-carrying wire decreases as the distance from the wire increases following inverse proportionality to the distance. At a point between two parallel wires, the magnetic field due to one wire is directly proportional to its current and inversely proportional to the distance from it, and the magnetic field due to the other wire is directly proportional to its current and inversely proportional to the distance from it, but in the opposite direction. Therefore, to find the point where the magnetic field is zero, we need to equate the magnetic field due to the two wires and solve for the distance.

Let the distance from the 3.0-A wire be x, then the distance from the 2.9-A wire is 10.0 - x. The magnetic field due to the 3.0-A wire at the point is:

B1 = μ0I1/2πx

The magnetic field due to the 2.9-A wire at the point is:

B2 = μ0I2/2π(10.0 - x)

Equating B1 and B2 and solving for x, we get:

x = (μ0I2/μ0I1 + I2) × 10.0 = (2.9/(3.0 + 2.9)) × 10.0 ≈ 5.1 cm

Therefore, the magnetic field is zero at a point 5.1 cm from the 3.0-A wire and 4.9 cm from the 2.9-A wire.

Question 5

The current in a long wire creates a magnetic field in the region around the wire.How is the strength of the field at distance r from the wire center related to the magnitude of the field?

Accepted Answer

The strength of the magnetic field at distance r from the wire center is inversely proportional to the distance r. This is governed by the inverse square law, which states that the strength of the magnetic field decreases with the square of the distance from the wire. Therefore, as distance increases, the strength of the magnetic field decreases.

Question 6

A high-voltage power line 23.0 m above the ground carries a current of 2 200 A.What is the magnetic field due to the current directly underneath the power line? (µ₀ = 4π × 10−⁷ T⋅m/A)

Accepted Answer

The magnetic field due to a long, straight conductor can be calculated using the formula $B = \frac{\mu_0 I}{2 \pi r}$, where $B$ is the magnetic field, $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}$), $I$ is the current, and $r$ is the distance from the conductor. Plugging in the given values: $B = \frac{4\pi \times 10^{-7} \times 2200}{2\pi \times 23}$, we find $B = 19.1 \, \mu\text{T}$.

Question 7

Niobium metal becomes a superconductor (with electrical resistance equal to zero)when cooled below 9.00 K.If superconductivity is destroyed when the surface magnetic field exceeds 0.100 T,determine the maximum current a 5.31-mm-diameter niobium wire can carry and remain superconducting.(µ₀ = 4π × 10−⁷ T⋅m/A)

Accepted Answer

The answer of Niobium metal becomes a superconductor (with electrical...

Question 8

A circular current loop is placed in an external magnetic field.How is the torque related to the radius of the loop?

Accepted Answer

The torque on a current loop in an external magnetic field is given by the formula T = NIAB sinθ, where N is the number of turns in the loop, I is the current, A is the area of the loop, B is the magnetic field, and θ is the angle between the magnetic field and the normal to the plane of the loop. Since the area of a circular loop is πr^2, we can write T = NI(πr^2)Bsinθ. Therefore, torque is directly proportional to the radius squared.

Question 9

Two long parallel wires 45.6 cm apart are carrying currents of 13.0 A and 23.0 A in the same direction.What is the magnitude of the magnetic field halfway between the wires?

Accepted Answer

The answer of Two long parallel wires 45.6 cm apart...

Question 10

A 10.0-m-long copper wire with cross-sectional area 1.25 × 10^-4 m² is bent into a square loop,and then connected to a 0.25-V battery.The loop is then placed in a uniform magnetic field of magnitude 0.19 T.What is the maximum torque that can act on this loop? The resistivity of copper is 1.70 × 10^-8Ω·m.

Accepted Answer

The maximum torque occurs when the magnetic field is perpendicular to the plane of the loop. The torque is given by:$$	au = IAB\sin	heta$$where I is the current, A is the area of the loop, B is the magnetic field, and θ is the angle between the magnetic field and the normal to the plane of the loop.The current is given by:$$I = \frac{V}{R}$$where V is the voltage and R is the resistance.The resistance is given by:$$R = \frac{ho L}{A}$$where ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.Substituting these equations into the equation for torque, we get:$$	au = \frac{VAB\sin	heta}{ho L}$$Plugging in the given values, we get:$$	au = \frac{(0.25 V)(1.25 	imes 10^{-4} m^2)(0.19 T)\sin 90^\circ}{1.70 	imes 10^{-8} \Omega \cdot m (10.0 m)}$$$$	au = 2.2 	imes 10^{-2} N \cdot m$$

Question 11

A circular loop carrying a current of 1.25 A is oriented in a magnetic field of 0.22 T.The loop has an area of 0.10 m² and is mounted on an axis,perpendicular to the magnetic field,which allows the loop to rotate.If the plane of the loop is oriented parallel to the field,what torque is created by the interaction of the loop current and the field?

Accepted Answer

The torque, τ, created by the interaction of the loop current and the magnetic field is given by the formula:

τ = NIA × B

where N is the number of turns in the loop (which is 1 in this case), I is the current in the loop, A is the area of the loop, B is the magnetic field, and × denotes the vector cross product.

When the loop is oriented parallel to the magnetic field, the angle between the normal to the loop (i.e. the axis of rotation) and the magnetic field is 0 degrees, so the torque is given by:

τ = NIA × B × sin(0°) = 0

Therefore, the correct answer is:

Answer: C
 When the loop is oriented parallel to the magnetic field, the torque created by the interaction of the loop current and the field is zero.

Question 12

A current in a long,straight wire produces a magnetic field.The magnetic field lines:

Accepted Answer

The magnetic field lines form circles that go around the wire. This can be demonstrated using the right-hand rule. If you wrap your right hand around the wire such that your thumb points in the direction of the current, the direction of the magnetic field lines will be in the direction of your fingers, which form circles around the wire.

Question 13

A square coil and a triangular coil each have sides of length L.The triangular coil has twice as many turns as the square coil.If a the same current is sent through each coil,when the coils are placed in the same uniform magnetic field making an angle of 30^° with the planes of the coils,which coil experiences the greater torque?

Accepted Answer

The torque experienced by a coil in a magnetic field is proportional to the number of turns, the area of the coil, and the sine of the angle between the magnetic field and the normal to the plane of the coil. The square coil has a larger area than the triangular coil, and since the triangular coil has twice as many turns, the square coil experiences the greater torque.

Question 14

Square coil A has 2N turns and sides of length L,and square coil B has N turns and sides of length 2L.When a current of 2 amps is sent through coil A and a current of 1 amp is sent through coil B,which coil has the greater magnetic moment?

Accepted Answer

The magnetic moment ($m$) of a coil is given by the product of the number of turns ($N$), the current ($I$), and the area ($A$) of the coil ($m = NIA$). For coil A, $m_A = 2N \times 2 \times L^2 = 4NL^2$. For coil B, $m_B = N \times 1 \times (2L)^2 = 4NL^2$. Thus, both coils have the same magnetic moment.

Question 15

A square loop of wire has a current going around it.The magnetic field from the current on each side of the loop results in a magnetic force on the wire on the opposite side.Each resulting magnetic force on the opposite side wire

Accepted Answer

The answer of A square loop of wire has a...

Question 16

Magnetism had been a known phenomenon for some time before its relation to electric currents was found.That a current in a wire produces a magnetic field was discovered by:

Accepted Answer

Oersted discovered that a current in a wire produces a magnetic field, this phenomenon is known as Oersted's law.

Question 17

There is a current I flowing in a clockwise direction in a square loop of wire that is in the plane of the paper.If the magnetic field B is toward the right,and if each side of the loop has length L,then the net magnetic torque acting on the loop is

Accepted Answer

The answer of There is a current I flowing in...

Question 18

A circular coil (radius = 0.25 m)has 143 turns and is in a uniform magnetic field.If the orientation of the coil is varied through all possible positions,the maximum torque on the coil by magnetic forces is 0.29 N⋅m when the current in the coil is 2.7 mA.What is the magnitude of the magnetic field?

Accepted Answer

The answer of A circular coil (radius = 0.25 m)has...

Question 19

A circular loop carrying a current of 1.6 A is oriented in a magnetic field of 0.30 T.The loop has an area of 0.14 m² and is mounted on an axis,perpendicular to the magnetic field,which allows the loop to rotate.What is the torque on the loop when its plane is oriented at a 21° angle to the field?

Accepted Answer

The torque on a current loop in a magnetic field is given by:$$	au = NIAB\sin	heta$$where:* N is the number of turns in the loop* I is the current in the loop* A is the area of the loop* B is the magnetic field strength* θ is the angle between the normal to the loop and the magnetic fieldIn this problem, we have:* N = 1* I = 1.6 A* A = 0.14 m^2* B = 0.30 T* θ = 21°Plugging these values into the equation, we get:$$	au = (1)(1.6 A)(0.14 m^2)(0.30 T)\sin(21°) = 2.4	imes10^{-2} N\cdot m$$Therefore, the correct answer is A.

Question 20

A rectangular coil (0.13 m × 0.98 m)has 277 turns and is in a uniform magnetic field of 0.50 T.If the orientation of the coil is varied through all possible positions,the maximum torque on the coil by magnetic forces is 0.096 N⋅m.What is the current in the coil?

Accepted Answer

The answer of A rectangular coil (0.13 m × 0.98...

Quiz 19: Magnetism

A 198-m-long wire carrying a current of 3.5 A will be accompanied by a magnetic field of what strength at a distance of 0.054 m from the wire? (magnetic permeability in empty space µ₀ = 4π × 10−⁷ T⋅m/A)

A superconducting wire carries a current of 7.0 kA.Find the magnetic field at a distance of 1.5 m from the wire.(µ₀ = 4π × 10−⁷ T⋅m/A)

Two long parallel wires 10.0 cm apart carry currents of 3.0 A and 2.9 A in the same direction.Is there any point between the two wires where the magnetic field is zero?

The current in a long wire creates a magnetic field in the region around the wire.How is the strength of the field at distance r from the wire center related to the magnitude of the field?

A high-voltage power line 23.0 m above the ground carries a current of 2 200 A.What is the magnetic field due to the current directly underneath the power line? (µ₀ = 4π × 10−⁷ T⋅m/A)

A circular current loop is placed in an external magnetic field.How is the torque related to the radius of the loop?

Two long parallel wires 45.6 cm apart are carrying currents of 13.0 A and 23.0 A in the same direction.What is the magnitude of the magnetic field halfway between the wires?

A current in a long,straight wire produces a magnetic field.The magnetic field lines:

Square coil A has 2N turns and sides of length L,and square coil B has N turns and sides of length 2L.When a current of 2 amps is sent through coil A and a current of 1 amp is sent through coil B,which coil has the greater magnetic moment?

A square loop of wire has a current going around it.The magnetic field from the current on each side of the loop results in a magnetic force on the wire on the opposite side.Each resulting magnetic force on the opposite side wire

Magnetism had been a known phenomenon for some time before its relation to electric currents was found.That a current in a wire produces a magnetic field was discovered by:

There is a current I flowing in a clockwise direction in a square loop of wire that is in the plane of the paper.If the magnetic field B is toward the right,and if each side of the loop has length L,then the net magnetic torque acting on the loop is

A circular loop carrying a current of 1.6 A is oriented in a magnetic field of 0.30 T.The loop has an area of 0.14 m² and is mounted on an axis,perpendicular to the magnetic field,which allows the loop to rotate.What is the torque on the loop when its plane is oriented at a 21° angle to the field?

A rectangular coil (0.13 m × 0.98 m) has 277 turns and is in a uniform magnetic field of 0.50 T.If the orientation of the coil is varied through all possible positions,the maximum torque on the coil by magnetic forces is 0.096 N⋅m.What is the current in the coil?

Quiz 19: Magnetism

A 198-m-long wire carrying a current of 3.5 A will be accompanied by a magnetic field of what strength at a distance of 0.054 m from the wire? (magnetic permeability in empty space µ0 = 4π × 10−7 T⋅m/A)

A superconducting wire carries a current of 7.0 kA.Find the magnetic field at a distance of 1.5 m from the wire.(µ0 = 4π × 10−7 T⋅m/A)

Two long parallel wires 10.0 cm apart carry currents of 3.0 A and 2.9 A in the same direction.Is there any point between the two wires where the magnetic field is zero?

The current in a long wire creates a magnetic field in the region around the wire.How is the strength of the field at distance r from the wire center related to the magnitude of the field?

A high-voltage power line 23.0 m above the ground carries a current of 2 200 A.What is the magnetic field due to the current directly underneath the power line? (µ0 = 4π × 10−7 T⋅m/A)

A circular current loop is placed in an external magnetic field.How is the torque related to the radius of the loop?

Two long parallel wires 45.6 cm apart are carrying currents of 13.0 A and 23.0 A in the same direction.What is the magnitude of the magnetic field halfway between the wires?

A current in a long,straight wire produces a magnetic field.The magnetic field lines:

Square coil A has 2N turns and sides of length L,and square coil B has N turns and sides of length 2L.When a current of 2 amps is sent through coil A and a current of 1 amp is sent through coil B,which coil has the greater magnetic moment?

A square loop of wire has a current going around it.The magnetic field from the current on each side of the loop results in a magnetic force on the wire on the opposite side.Each resulting magnetic force on the opposite side wire

Magnetism had been a known phenomenon for some time before its relation to electric currents was found.That a current in a wire produces a magnetic field was discovered by:

There is a current I flowing in a clockwise direction in a square loop of wire that is in the plane of the paper.If the magnetic field B is toward the right,and if each side of the loop has length L,then the net magnetic torque acting on the loop is

A circular loop carrying a current of 1.6 A is oriented in a magnetic field of 0.30 T.The loop has an area of 0.14 m2 and is mounted on an axis,perpendicular to the magnetic field,which allows the loop to rotate.What is the torque on the loop when its plane is oriented at a 21° angle to the field?

A rectangular coil (0.13 m × 0.98 m) has 277 turns and is in a uniform magnetic field of 0.50 T.If the orientation of the coil is varied through all possible positions,the maximum torque on the coil by magnetic forces is 0.096 N⋅m.What is the current in the coil?

A 198-m-long wire carrying a current of 3.5 A will be accompanied by a magnetic field of what strength at a distance of 0.054 m from the wire? (magnetic permeability in empty space µ₀ = 4π × 10−⁷ T⋅m/A)

A superconducting wire carries a current of 7.0 kA.Find the magnetic field at a distance of 1.5 m from the wire.(µ₀ = 4π × 10−⁷ T⋅m/A)

A high-voltage power line 23.0 m above the ground carries a current of 2 200 A.What is the magnetic field due to the current directly underneath the power line? (µ₀ = 4π × 10−⁷ T⋅m/A)