Question 1

Two long straight wires each carry a current of $12 \mathrm{~A}$. One wire lies on the $\mathrm{x}$-axis with its current in the positive $\mathrm{x}$-direction. The other wire lies on the $\mathrm{y}$-axis with its current in the positive $\mathrm{y}$-direction. In the $\mathrm{x}-\mathrm{y}$ plane, which quadrant (quadrants) has/have points where the magnetic field is zero?

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Question 2

One  wire, lying on the $x$-axis, carries a current of $8.0 \mathrm{~A}$ in the positive $x$-direction. Another wire, lying on the $\mathrm{y}$-axis, carries a current of $12 \mathrm{~A}$ in the positive $\mathrm{y}$-direction. What is the magnitude of the magnetic field at ( $\mathrm{x}$, y) $=(8.0 \mathrm{~cm}, 12.0 \mathrm{~cm})$ ?

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Question 3

A solenoid of radius $1.1 \mathrm{~cm}$, carrying a current of $2.2 \mathrm{~A}$, produces a magnetic field at its center of $0.28 \mathrm{~T}$. How many turns per unit length does the solenoid have?

Accepted Answer

The magnetic field at the center of a solenoid is given by:$$B = \mu_0 n I$$where:* $B$ is the magnetic field* $\mu_0$ is the permeability of free space* $n$ is the number of turns per unit length* $I$ is the currentSolving for $n$, we get:$$n = \frac{B}{\mu_0 I}$$Plugging in the given values, we get:$$n = \frac{0.28 \mathrm{~T}}{4\pi \times 10^{-7} \mathrm{~T \cdot m/A} \times 2.2 \mathrm{~A}} = 1.0 \times 10^{5} \mathrm{~m}^{-1}$$Therefore, the correct answer is A.

Question 4

Find the circulation for the path shown.

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Question 5

Find the circulation for the path shown.

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Question 6

A proton and electron, each travelling with the same velocity, enter a region of uniform magnetic field. They experience

Accepted Answer

The force on a charged particle in a magnetic field is given by $F = qvB\sin(\theta)$, where $q$ is the charge, $v$ is the velocity, $B$ is the magnetic field strength, and $\theta$ is the angle between the velocity and the magnetic field. Since the proton and electron have equal and opposite charges and are moving with the same velocity, they experience forces of equal magnitude but in opposite directions due to their opposite charges.

Question 7

A proton and electron, travelling with the same velocity in the $+x$ direction, enter separate regions, each with a uniform magnetic field in the $\pm \mathrm{y}$ direction (magnitude $\mathrm{B}_{\mathrm{p}}$ for the proton, $\mathrm{B}_{\mathrm{e}}$ for the electron). They each experience the same acceleration. What can we conclude?

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Question 8

A proton and electron, each travelling with the same velocity in the $+x$ direction, enter a region of uniform magnetic field in the $+y$ direction. If the acceleration of the electron is $a$ in the $+z$ direction, what is the acceleration of the proton?

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Question 9

A cyclotron is designed to accelerate protons (mass $1.67 \times 10^{-27} \mathrm{~kg}$ ) up to a kinetic energy of $2.5 \times 10^{-13} \mathrm{~J}$. If the magnetic field in the cyclotron is $0.75 \mathrm{~T}$, what is the radius of the dipole magnets in the cyclotron?

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Question 10

A cyclotron is designed to accelerate protons (mass $1.67 \times 10^{-27} \mathrm{~kg}$ ) up to a kinetic energy of $2.5 \times 10^{-13} \mathrm{~J}$. If the radius of the dipole magnets is $96 \mathrm{~cm}$, what is the magnetic field used in the cyclotron?

Accepted Answer

The kinetic energy of a proton is given by:$$K = \frac{1}{2}mv^2$$where $m$ is the mass of the proton and $v$ is its speed. The magnetic force on a proton is given by:$$F = qvB$$where $q$ is the charge of the proton, $v$ is its speed, and $B$ is the magnetic field strength. The centripetal force on a proton is given by:$$F_c = \frac{mv^2}{r}$$where $r$ is the radius of the circular path. In a cyclotron, the magnetic force and the centripetal force are equal, so we can set these two equations equal to each other and solve for $B$:$$qvB = \frac{mv^2}{r}$$$$B = \frac{mv}{qr}$$Plugging in the given values, we get:$$B = \frac{(1.67 \times 10^{-27} \mathrm{~kg})(2.5 \times 10^{-13} \mathrm{~J})}{(1.6 \times 10^{-19} \mathrm{C})(0.96 \mathrm{~m})}$$$$B = 0.19 \mathrm{~T}$$Therefore, the correct answer is D) $0.19 \mathrm{~T}$.

Question 11

A cyclotron is designed to accelerate protons to a maximum kinetic energy K. Assuming one then tried to accelerate alpha particles (about four times the mass and twice the charge), what kinetic energy could be achieved?

Accepted Answer

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Question 12

A charged particle of mass $1.0 \times 10^{-26} \mathrm{~kg}$ enters a region of uniform magnetic field at a speed of $2.8 \times 10^{6}$ $\mathrm{m} / \mathrm{s}$, at an angle of 37 degrees relative to the magnetic field direction. If the magnetic field strength is $1.2 \mathrm{~T}$ and the charge of the particle is $+\mathrm{e}$, what will be the radius of the helical path it takes?

Accepted Answer

The radius $r$ of the helical path of a charged particle moving in a magnetic field is given by the formula $r = \frac{mv\sin\theta}{qB}$, where $m$ is the mass of the particle, $v$ is its velocity, $\theta$ is the angle of the velocity vector with the magnetic field, $q$ is the charge of the particle, and $B$ is the magnetic field strength. Given $m = 1.0 \times 10^{-26} \mathrm{~kg}$, $v = 2.8 \times 10^{6} \mathrm{~m/s}$, $\theta = 37^\circ$, $q = +e = 1.6 \times 10^{-19} \mathrm{~C}$, and $B = 1.2 \mathrm{~T}$, substituting these values into the formula gives a radius of approximately $8.8 \mathrm{~cm}$.

Question 13

A charged particle of mass $1.0 \times 10^{-26} \mathrm{~kg}$ enters a region of uniform magnetic field at a speed of $2.8 \times 10^{6}$ $\mathrm{m} / \mathrm{s}$, at an angle of 37 degrees relative to the magnetic field direction. If the magnetic field strength is $1.2 \mathrm{~T}$ what will be the radius of the helical path it takes?

Accepted Answer

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Quiz 19: Magnetic Forces and Fields

A solenoid of radius $1.1 \mathrm{~cm}$ , carrying a current of $2.2 \mathrm{~A}$ , produces a magnetic field at its center of $0.28 \mathrm{~T}$ . How many turns per unit length does the solenoid have?

Find the circulation for the path shown. $Find the circulation for the path shown. A) -(4 A ) \mu_{0} B) -\left(28\right. A) \mu_{0} C) (28 \mathrm{~A}) \mu_{0} D) (4 \mathrm{~A}) \mu_{0} E) (7 \mathrm{~A}) \mu_{0}$

Find the circulation for the path shown. $Find the circulation for the path shown. A) \left(4\right. A) \mu_{0} B) -(28 \mathrm{~A}) \mu_{0} C) (28 \mathrm{~A}) \mu_{0} D) -(4 \mathrm{~A}) \mu_{0} E) -(7 \mathrm{~A}) \mu_{0}$

A proton and electron, each travelling with the same velocity, enter a region of uniform magnetic field. They experience

A proton and electron, each travelling with the same velocity in the $+x$ direction, enter a region of uniform magnetic field in the $+y$ direction. If the acceleration of the electron is $a$ in the $+z$ direction, what is the acceleration of the proton?

A cyclotron is designed to accelerate protons (mass $1.67 \times 10^{-27} \mathrm{~kg}$ ) up to a kinetic energy of $2.5 \times 10^{-13} \mathrm{~J}$ . If the magnetic field in the cyclotron is $0.75 \mathrm{~T}$ , what is the radius of the dipole magnets in the cyclotron?

A cyclotron is designed to accelerate protons (mass $1.67 \times 10^{-27} \mathrm{~kg}$ ) up to a kinetic energy of $2.5 \times 10^{-13} \mathrm{~J}$ . If the radius of the dipole magnets is $96 \mathrm{~cm}$ , what is the magnetic field used in the cyclotron?

A cyclotron is designed to accelerate protons to a maximum kinetic energy K. Assuming one then tried to accelerate alpha particles (about four times the mass and twice the charge) , what kinetic energy could be achieved?

Quiz 19: Magnetic Forces and Fields

A solenoid of radius 1.1 cm1.1 \mathrm{~cm}1.1 cm , carrying a current of 2.2 A2.2 \mathrm{~A}2.2 A , produces a magnetic field at its center of 0.28 T0.28 \mathrm{~T}0.28 T . How many turns per unit length does the solenoid have?

Find the circulation for the path shown.

Find the circulation for the path shown.

A proton and electron, each travelling with the same velocity, enter a region of uniform magnetic field. They experience

A proton and electron, each travelling with the same velocity in the +x+x+x direction, enter a region of uniform magnetic field in the +y+y+y direction. If the acceleration of the electron is aaa in the +z+z+z direction, what is the acceleration of the proton?

A cyclotron is designed to accelerate protons to a maximum kinetic energy K. Assuming one then tried to accelerate alpha particles (about four times the mass and twice the charge) , what kinetic energy could be achieved?

A solenoid of radius $1.1 \mathrm{~cm}$ , carrying a current of $2.2 \mathrm{~A}$ , produces a magnetic field at its center of $0.28 \mathrm{~T}$ . How many turns per unit length does the solenoid have?

Find the circulation for the path shown. $Find the circulation for the path shown. A) -(4 A ) \mu_{0} B) -\left(28\right. A) \mu_{0} C) (28 \mathrm{~A}) \mu_{0} D) (4 \mathrm{~A}) \mu_{0} E) (7 \mathrm{~A}) \mu_{0}$

Find the circulation for the path shown. $Find the circulation for the path shown. A) \left(4\right. A) \mu_{0} B) -(28 \mathrm{~A}) \mu_{0} C) (28 \mathrm{~A}) \mu_{0} D) -(4 \mathrm{~A}) \mu_{0} E) -(7 \mathrm{~A}) \mu_{0}$

A proton and electron, each travelling with the same velocity in the $+x$ direction, enter a region of uniform magnetic field in the $+y$ direction. If the acceleration of the electron is $a$ in the $+z$ direction, what is the acceleration of the proton?