Question 1

A coil of wire 20 cm length and 200 turns carries a current of 10 A.A bar of titanium (magnetic susceptibility 1.81 x 10^-4)is positioned within the coil.The magnetic field inside the titanium bar is

Accepted Answer

The magnetic field inside the titanium bar can be calculated using the formula for the magnetic field inside a material, which is $B = \mu H$, where $\mu = \mu_0(1 + \chi)$ and $H$ is the magnetic field due to the current in the coil. For a coil, $H = nI$, where $n$ is the number of turns per unit length and $I$ is the current. Given that the coil has 200 turns and a length of 20 cm (0.2 m), $n = 200 / 0.2 = 1000$ turns/m. With $I = 10$ A, $H = 1000 \times 10 = 10000$ A/m. The magnetic susceptibility of titanium ($\chi$) is $1.81 \times 10^{-4}$, and $\mu_0 = 4\pi \times 10^{-7}$ Tm/A. Thus, $\mu = 4\pi \times 10^{-7} \times (1 + 1.81 \times 10^{-4})$, and the magnetic field $B = \mu H = 4\pi \times 10^{-7} \times (1 + 1.81 \times 10^{-4}) \times 10000$, which calculates to approximately $1.257 \times 10^{-2}$ T, matching option D.

Question 2

A square,clamping ammeter has four sides each with a length of 3.0 cm.The four sides of the ammeter are capable of measuring the magnetic field at the position of the sides.When the ammeter is clamped around a cylindrical wire carrying a 5.0 A DC current as shown in the figure,what is the average magnetic field measured in the sides of the clamp?

Accepted Answer

The magnetic field at the position of the sides of the ammeter can be calculated using the formula:
B = μ0 * I / (2 * r)

where B is the magnetic field, μ0 is the permeability of free space (4π x 10^-7 T·m/A), I is the current, and r is the distance between the wire and the side of the clamp.

Since the wire is cylindrical, the distance between the wire and each side of the clamp is 1.5 cm (half of the side length).

Therefore, the magnetic field measured in each side of the clamp is:
B = μ0 * I / (2 * r) = (4π x 10^-7) * 5.0 / (2 * 0.015) = 0.52 G

The average magnetic field measured in the sides of the clamp is simply the average of the four measurements, which is also 0.52 G. Therefore, the best choice is C.

Question 3

The figure shows the cross section through 3 long wires with linear mass density 100 g/m.They carry currents I₁,I₂,and I₃ in the directions shown.Wires 2 and 3 are 10 cm apart and are attached to a vertical surface,and each carry a current of 600 A.What current I₁ will allow wire 1 on the right to "float" such that its distance from the vertical surface is 10 cm?

Accepted Answer

Using the formula for the magnetic field created by a long wire, we can find the force per unit length on wire 1 caused by wires 2 and 3:
F/L = μ0 * I2 * I1 / (2πd)
where μ0 is the permeability of free space, I2 is the current in wires 2 and 3 (both 600 A), I1 is the unknown current in wire 1, and d is the distance between wires 2 and 3 (10 cm = 0.1 m). Since wire 1 is "floating", the force per unit length must be zero, so we can set F/L to zero and solve for I1:
0 = μ0 * 600 A * I1 / (2π * 0.1 m)
Solving for I1 gives I1 = 1021 A, which is choice A.

Question 4

Two wires carry different currents in the opposite directions as shown.Where is it possible for the magnetic field produced by the wires to be zero?

Accepted Answer

According to the right-hand rule, the magnetic field produced by a current-carrying wire will form concentric circles around the wire. At point A, the magnetic field produced by both wires will be in the opposite direction and cancel each other out, resulting in a zero magnetic field. Similarly at point C, the magnetic field produced by both wires will be in the same direction and add up to cancel each other out, resulting in a zero magnetic field. Therefore, the correct answer is D) A or C only.

Question 5

Two 100 turn coils of wire with a diameter of 1.0 m are placed a distance of 0.25 m apart as shown in the figure.A current of 3.0 A is in the wires of both coils and the direction of the current is clockwise (CW)for both coils when viewed from one end.What is the magnitude of the magnetic field in the center between the two coils?

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The answer of Two 100 turn coils of wire with...

Question 6

A particle with a mass of 1 mg and a charge q is seen to travel with a speed of 1000 m/s parallel to a straight current carrying wire along a horizontal path 10 cm below the wire as shown in the figure.Determine q if the magnitude of current in the wire is 10 A.

Accepted Answer

The force on a charged particle moving with velocity v, in a magnetic field of intensity B, is given by the formula F=qvB. 
In this problem, the wire carrying current produces a magnetic field B at the location of the particle, which is moving parallel to the wire. The force on the particle is thus perpendicular to its velocity and the wire, and points towards the wire. 
Using the given distance of 10 cm and applying the right-hand rule, we can determine that the magnetic field produced by the current-carrying wire has a magnitude of 2 x 10^-5 T at the location of the particle. 
The force on the particle is then F = qvB = m*a, where m is the mass of the particle, a is its acceleration, and v and B are as given above. Solving for q gives q = m*a/(v*B) = (1x10^-6 kg)(9.81 m/s^2)/(1000 m/s)(2x10^-5 T) = 0.49 C. 
Therefore, the answer is B.

Question 7

A long,straight wire is located along the x-axis (y = 0 and z = 0).The wire carries a current of 5.0 A in the +x direction.What is the magnitude of the force on a 2.0 C charged particle located at (+2.0 m,+1.0 m,0),when it has a velocity of 300 m/s in the +z-direction?

Accepted Answer

The force on a charged particle moving in a magnetic field is given by the Lorentz force equation, $F = q(\vec{v} \times \vec{B})$, where $q$ is the charge, $\vec{v}$ is the velocity of the particle, and $\vec{B}$ is the magnetic field. Since the particle is moving in the +z direction and the current is in the +x direction, the magnetic field at the location of the particle due to the current in the wire would be in the plane perpendicular to the direction of the current (in this case, in the y-z plane). However, since the particle's velocity is parallel to the direction of the magnetic field lines (both in the z direction), the cross product $\vec{v} \times \vec{B}$ is zero, resulting in a force of 0.0 N.

Question 8

A very long wire carrying a current I = 5.0 A is bent into a semi-circle with a diameter of 10 cm as shown in the figure.What is the magnitude of the magnetic field at the point P,halfway between the ends of the straight sections of wire and at the center of curvature of the semi-circle?

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The answer of A very long wire carrying a current...

Question 9

A long wire located at Z = 0 carries current i₁ = 3.00 A to the right as shown.A second long wire located a distance d = 0.240 m above the first wire carries a current i₂ = 1.10 A to the left as shown.Where in the Z direction (in m)does the magnetic field from the two wires sum to zero?

Accepted Answer

The answer of A long wire located at Z =...

Question 10

A square,clamping ammeter has four sides each with a length of 3.0 cm.The four sides of the ammeter are capable of measuring the magnetic field at the position of the sides.When the ammeter is clamped around a cylindrical wire carrying a DC current as shown in the figure,the average magnetic field measured in the sides of the clamp is 2.0

Accepted Answer

The answer of A square,clamping ammeter has four sides each...

Question 11

A solenoid is made up of 100 turns of a wire carrying 0.25 A of current,and is 5.0 cm long.The radius of the solenoid is 1.5cm.You are looking at the solenoid end-on,such that the current circulates counter-clockwise from your point of view.A complete circuit is made by having the wire from one end of the solenoid connect to the wire at the other end,and running down the middle of the solenoid,therefore carrying current in the +z direction along the z-axis.What is the magnetic field at a point (x,y)= (-0.75 cm,0.0 cm)?

Accepted Answer

Using the formula for the magnetic field inside a solenoid, 
B = μ₀nI,
where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current. 
n = N/L = 100/0.05 = 2000 turns/meter 
B = (4π×10⁻⁷ T·m/A)·(2000 turns/m)·(0.25 A) = 0.628 T

Since the magnetic field is parallel to the z-axis, we can find the field at the given point by calculating the distance to the z-axis and multiplying by the field strength. 
The distance from the point (-0.75cm,0cm) to the z-axis is 0.75 cm. 
Therefore, 
B = (0.75 cm)(0.628 T) = 0.471 T

The magnetic field at the point is therefore 0.471 T in the -x direction.

Question 12

A wire of radius R = 4 mm carries a uniformly distributed current of 2 A.The magnetic field inside the wire at a radial distance R/2 from the axis of the wire is

Accepted Answer

The magnetic field inside a wire carrying a uniformly distributed current is given by B = (μ₀ * I * r) / (2π * R²), where r is the radial distance from the axis. Substituting the given values, B = (4π * 10⁻⁷ T*m/A * 2 A * 2 mm) / (2π * (4 mm)²) = 5 * 10⁻⁵ T.

Question 13

Two long wires (mass per unit length 1.9 g/m)are suspended by threads attached from the ceiling so that they are parallel to each other and to the ceiling above.They each carry an electric current of 15A,in opposite directions.When they carry no current,the wires hang such that they are touching all along their length,and the threads are vertical and immediately adjacent to one another.If the angle between the threads is 10.0S1U1P1$\circ$S1S1P0,what is the length of the threads from which the wires hang?

Accepted Answer

The force between the two wires causes them to separate, creating tension in the threads. The tension in each thread is given by:
T = mg(secθ/2) 
where m is the mass per unit length of the wire, g is acceleration due to gravity, and θ is the angle between the threads.

The force between the wires is given by:
F = μ₀I₁I₂L/2πr 
where μ₀ is the permeability of free space, I₁ and I₂ are the currents in the wires, L is the length of the wires, and r is the distance between them.

Since the wires are touching and parallel, their separation is negligible and r can be taken as zero. This gives:
F = μ₀I₁I₂L/2π(0) = ∞
which means that the wires would repel each other infinitely if they were free to move. However, they are constrained by the threads.

The tension in each thread must be equal to half the force between the wires:
T = F/2
T = μ₀I₁I₂L/4πd 
where d is the separation between the threads.

Setting the tensions equal to each other and solving for L:
mg(secθ/2) = μ₀I₁I₂L/4πd 
L = 2dmg(secθ/2)/(μ₀I₁I₂)

Substituting in the given values, we get:
L = 0.16 m

Question 14

The overhead cable for a street trolley is strung horizontally 5 m above the ground.A long straight section of it carries a 100 A current due west.What is the magnetic field due to the current in the cable at street level directly under the cable?

Accepted Answer

The magnetic field due to a current-carrying conductor can be calculated using the right-hand rule and the formula B = μ₀I/(2πr), where μ₀ = 4π x 10^-7 Tm/A, I = 100 A, and r = 5 m. The direction is perpendicular to the plane formed by the current direction and the line from the point to the wire, which means it points south in this case.

Question 15

Two parallel wires,separated by the distance of 2 cm,carry the currents I₁ = 1 A and I₂ = 2 A in the same direction.How far from the wire carrying the current I₁ is the magnetic field zero?

Accepted Answer

The magnetic field at a point between two parallel wires carrying currents in the same direction can be found using the formula: B = μ0*I/(2π*d) where B is the magnetic field, μ0 is the permeability of free space, I is the current, and d is the distance between the wires. For the current I₁, the magnetic field will be zero at a distance of: d = μ0*I/(2π*B) d = μ0*1/(2π*(1.2567*10^-6)*1)/(10^-2) d = 0.6667 cm Therefore, the magnetic field will be zero at a distance of 0.6667 cm from the wire carrying the current I₁.

Question 16

Two long wires are suspended by 16-cm long threads attached from the ceiling so that they are parallel to each other and to the ceiling above.They each carry an electric current of 15A,in opposite directions.When they carry no current,the wires hang such that they are touching all along their length,and the threads are vertical and immediately adjacent to one another.If the angle between the threads is 10.0S1U1P1$\circ$S1S1P0,what is the mass per unit length of the wires?

Accepted Answer

The answer of Two long wires are suspended by 16-cm...

Question 17

A long,straight wire is located along the x-axis (y = 0 and z = 0).The wire carries a current of 5.0 A in the +x direction.What is the magnitude of the force on a 2.0 C charged particle located at (+2.0 m,+1.0 m,0),when it has a velocity of 300 m/s in the +x-direction?

Accepted Answer

The answer of A long,straight wire is located along the...

Question 18

Two long wires lie parallel to the x-axis;one at y = 0.0 m,the other at y = 0.12 m.The first carries current of 1.0 A in the positive x direction,while the other carries current of 1.5 A in the negative x direction.Which of the below is a y-coordinate value at which there is no magnetic field?

Accepted Answer

The answer of Two long wires lie parallel to the...

Quiz 28: Magnetic Fields of Moving Charges

A coil of wire 20 cm length and 200 turns carries a current of 10 A.A bar of titanium (magnetic susceptibility 1.81 x 10^-4) is positioned within the coil.The magnetic field inside the titanium bar is

Two wires carry different currents in the opposite directions as shown.Where is it possible for the magnetic field produced by the wires to be zero?

A particle with a mass of 1 mg and a charge q is seen to travel with a speed of 1000 m/s parallel to a straight current carrying wire along a horizontal path 10 cm below the wire as shown in the figure.Determine q if the magnitude of current in the wire is 10 A.

A long,straight wire is located along the x-axis (y = 0 and z = 0) .The wire carries a current of 5.0 A in the +x direction.What is the magnitude of the force on a 2.0 C charged particle located at (+2.0 m,+1.0 m,0) ,when it has a velocity of 300 m/s in the +z-direction?

A very long wire carrying a current I = 5.0 A is bent into a semi-circle with a diameter of 10 cm as shown in the figure.What is the magnitude of the magnetic field at the point P,halfway between the ends of the straight sections of wire and at the center of curvature of the semi-circle?

A long wire located at Z = 0 carries current i₁ = 3.00 A to the right as shown.A second long wire located a distance d = 0.240 m above the first wire carries a current i₂ = 1.10 A to the left as shown.Where in the Z direction (in m) does the magnetic field from the two wires sum to zero?

A wire of radius R = 4 mm carries a uniformly distributed current of 2 A.The magnetic field inside the wire at a radial distance R/2 from the axis of the wire is

The overhead cable for a street trolley is strung horizontally 5 m above the ground.A long straight section of it carries a 100 A current due west.What is the magnetic field due to the current in the cable at street level directly under the cable?

Two parallel wires,separated by the distance of 2 cm,carry the currents I₁ = 1 A and I₂ = 2 A in the same direction.How far from the wire carrying the current I₁ is the magnetic field zero?

A long,straight wire is located along the x-axis (y = 0 and z = 0) .The wire carries a current of 5.0 A in the +x direction.What is the magnitude of the force on a 2.0 C charged particle located at (+2.0 m,+1.0 m,0) ,when it has a velocity of 300 m/s in the +x-direction?

Two long wires lie parallel to the x-axis;one at y = 0.0 m,the other at y = 0.12 m.The first carries current of 1.0 A in the positive x direction,while the other carries current of 1.5 A in the negative x direction.Which of the below is a y-coordinate value at which there is no magnetic field?

Quiz 28: Magnetic Fields of Moving Charges

A coil of wire 20 cm length and 200 turns carries a current of 10 A.A bar of titanium (magnetic susceptibility 1.81 x 10-4) is positioned within the coil.The magnetic field inside the titanium bar is

Two wires carry different currents in the opposite directions as shown.Where is it possible for the magnetic field produced by the wires to be zero?

A particle with a mass of 1 mg and a charge q is seen to travel with a speed of 1000 m/s parallel to a straight current carrying wire along a horizontal path 10 cm below the wire as shown in the figure.Determine q if the magnitude of current in the wire is 10 A.

A long,straight wire is located along the x-axis (y = 0 and z = 0) .The wire carries a current of 5.0 A in the +x direction.What is the magnitude of the force on a 2.0 C charged particle located at (+2.0 m,+1.0 m,0) ,when it has a velocity of 300 m/s in the +z-direction?

A very long wire carrying a current I = 5.0 A is bent into a semi-circle with a diameter of 10 cm as shown in the figure.What is the magnitude of the magnetic field at the point P,halfway between the ends of the straight sections of wire and at the center of curvature of the semi-circle?

A long wire located at Z = 0 carries current i1 = 3.00 A to the right as shown.A second long wire located a distance d = 0.240 m above the first wire carries a current i2 = 1.10 A to the left as shown.Where in the Z direction (in m) does the magnetic field from the two wires sum to zero?

A wire of radius R = 4 mm carries a uniformly distributed current of 2 A.The magnetic field inside the wire at a radial distance R/2 from the axis of the wire is

The overhead cable for a street trolley is strung horizontally 5 m above the ground.A long straight section of it carries a 100 A current due west.What is the magnetic field due to the current in the cable at street level directly under the cable?

Two parallel wires,separated by the distance of 2 cm,carry the currents I1 = 1 A and I2 = 2 A in the same direction.How far from the wire carrying the current I1 is the magnetic field zero?

A long,straight wire is located along the x-axis (y = 0 and z = 0) .The wire carries a current of 5.0 A in the +x direction.What is the magnitude of the force on a 2.0 C charged particle located at (+2.0 m,+1.0 m,0) ,when it has a velocity of 300 m/s in the +x-direction?

Two long wires lie parallel to the x-axis;one at y = 0.0 m,the other at y = 0.12 m.The first carries current of 1.0 A in the positive x direction,while the other carries current of 1.5 A in the negative x direction.Which of the below is a y-coordinate value at which there is no magnetic field?

A coil of wire 20 cm length and 200 turns carries a current of 10 A.A bar of titanium (magnetic susceptibility 1.81 x 10^-4) is positioned within the coil.The magnetic field inside the titanium bar is

A long wire located at Z = 0 carries current i₁ = 3.00 A to the right as shown.A second long wire located a distance d = 0.240 m above the first wire carries a current i₂ = 1.10 A to the left as shown.Where in the Z direction (in m) does the magnetic field from the two wires sum to zero?

Two parallel wires,separated by the distance of 2 cm,carry the currents I₁ = 1 A and I₂ = 2 A in the same direction.How far from the wire carrying the current I₁ is the magnetic field zero?