Question 1

In a mass spectrometer ions of Ni with mass 9.62 $\times$ 10^-26 kg and charge +2e are accelerated through a potential difference of X volts and then deflected in a magnetic field of 0.15 T.If the radius of curvature of the ions is 0.55 m,then calculate the value of the potential difference X.

Accepted Answer

The answer of In a mass spectrometer ions of Ni...

Question 2

Use the diagram for the next problem. 
-A circular current loop lies in the xy plane and has radius R = 10 cm.The loop has 20 turns and carries a current I = 4 A.A magnetic field of strength 0.3 T is applied at an angle of $\theta$ = 30S1U1P1$\circ$S1S1P0 to the loop.The potential energy of the magnetic dipole is

Accepted Answer

The potential energy $U$ of a magnetic dipole in a magnetic field is given by $U = -\mu B \cos(\theta)$, where $\mu$ is the magnetic moment, $B$ is the magnetic field strength, and $\theta$ is the angle between the magnetic moment and the magnetic field. The magnetic moment $\mu$ is given by $NIA$, where $N$ is the number of turns, $I$ is the current, and $A$ is the area of the loop. Given $N = 20$, $I = 4$ A, $R = 0.1$ m, and $B = 0.3$ T, with $\theta = 30^\circ$, we find $A = \pi R^2 = \pi (0.1)^2$, and thus $\mu = NIA = 20 \times 4 \times \pi (0.1)^2$. Substituting these values into the formula for $U$, and using $\cos(30^\circ) = \sqrt{3}/2$, we find $U = -\mu B \cos(30^\circ)$, which calculates to approximately $0.163$ J.

Question 3

A small permanent magnet is placed in a uniform magnetic field of magnitude 0.35 T.If the maximum torque experienced by the magnet is 0.50 N · m,what is the magnitude of the magnetic moment of the magnet?

Accepted Answer

The maximum torque ($\tau$) experienced by a magnet in a uniform magnetic field is given by the equation $\tau = \mu B \sin(\theta)$, where $\mu$ is the magnetic moment of the magnet, $B$ is the magnetic field strength, and $\theta$ is the angle between the magnetic moment and the magnetic field. The maximum torque occurs when $\sin(\theta) = 1$ (i.e., $\theta = 90^\circ$). Therefore, the equation simplifies to $\tau = \mu B$. Rearranging for $\mu$, we get $\mu = \tau / B$. Substituting the given values, $\mu = 0.50 \, \text{N} \cdot \text{m} / 0.35 \, \text{T} = 1.43 \, \text{A} \cdot \text{m}^2$, which rounds to 1.4 A·m^2, making option A correct.

Question 4

A circular,20-turn coil has a radius of 5.0 cm.What is the magnitude of the magnetic moment of the coil when it carries a current of 2.5 A?

Accepted Answer

The answer of A circular,20-turn coil has a radius of...

Question 5

A beam of charged particles moving with a speed of 10⁶ m/s enters a uniform magnetic field of 0.1 T at right angles to the direction of motion.If the particles move in a radius of 0.2 m,then calculate their period of motion.

Accepted Answer

The period of motion T for a charged particle in a magnetic field is given by T = 2πm/qB. Using the relation v = rω = rqB/m, we find T = 2πr/v. Substituting r = 0.2 m and v = 10^6 m/s, we get T = 2π(0.2)/(10^6) = 1.3 × 10^-6 s.

Question 6

Which of the following statements correctly describes the torque-potential energy relationship for a current-carrying coil in a uniform magnetic field?

Accepted Answer

The torque on a current-carrying coil in a uniform magnetic field acts to align the magnetic moment of the coil with the magnetic field, which corresponds to a position of lower potential energy. This is because systems tend to move towards configurations that minimize their potential energy.

Question 7

An alpha particle with a charge 2e and mass 4m is moving with velocity v when it enters a magnetic field B at right angles to its direction of motion.A deuteron of charge e and mass 2m also enters the field in the same direction and the same speed.Calculate the difference in radius of motion between the alpha particle and the deuteron in the magnetic field region.

Accepted Answer

The answer of An alpha particle with a charge 2e...

Question 8

A circular,20-turn coil of radius 5.0 cm is oriented in such a way that its axis makes a 30º angle with a uniform magnetic field of 0.15 T.What is the torque on the coil when it carries a current of 2.5 A?

Accepted Answer

The answer of A circular,20-turn coil of radius 5.0 cm...

Question 9

When a compass needle is in stable equilibrium in a magnetic field  ,

Accepted Answer

The answer of When a compass needle is in stable...

Question 10

The angle through which the pointer on a galvanometer rotates is

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The answer of The angle through which the pointer on...

Question 11

Use the diagram for the next problem. 
-A circular current loop lies in the xy plane and has radius R = 10 cm.The loop has 20 turns and carries a current I = 4 A.The magnetic dipole of the loop is

Accepted Answer

The answer of Use the diagram for the next problem....

Question 12

A beam of electrons moving at a speed of 8 $\times$ 10⁴ m/s is undeflected when it passes through an electric field of 5 N/C perpendicular to its path and a magnetic field that is perpendicular to its path and also to that of the electric field.Calculate the strength of the magnetic field.

Accepted Answer

For an electron beam to be undeflected by perpendicular electric and magnetic fields, the force due to the electric field (F_e = qE) must equal the force due to the magnetic field (F_m = qvB). Setting these equal gives E = vB, solving for B gives B = E/v. Substituting E = 5 N/C and v = 8×10^6 m/s gives B = 5/(8×10^6) = 6.25×10^-7 T.

Question 13

A compass needle is in a homogeneous magnetic field  with its south pole pointing in the positive direction of  .The net force on the compass needle is

Accepted Answer

The answer of A compass needle is in a homogeneous...

Quiz 26: The Magnetic Field

In a mass spectrometer ions of Ni with mass 9.62 ×\times× 10-26 kg and charge +2e are accelerated through a potential difference of X volts and then deflected in a magnetic field of 0.15 T.If the radius of curvature of the ions is 0.55 m,then calculate the value of the potential difference X.

A small permanent magnet is placed in a uniform magnetic field of magnitude 0.35 T.If the maximum torque experienced by the magnet is 0.50 N · m,what is the magnitude of the magnetic moment of the magnet?

A circular,20-turn coil has a radius of 5.0 cm.What is the magnitude of the magnetic moment of the coil when it carries a current of 2.5 A?

A beam of charged particles moving with a speed of 106 m/s enters a uniform magnetic field of 0.1 T at right angles to the direction of motion.If the particles move in a radius of 0.2 m,then calculate their period of motion.

Which of the following statements correctly describes the torque-potential energy relationship for a current-carrying coil in a uniform magnetic field?

A circular,20-turn coil of radius 5.0 cm is oriented in such a way that its axis makes a 30º angle with a uniform magnetic field of 0.15 T.What is the torque on the coil when it carries a current of 2.5 A?

When a compass needle is in stable equilibrium in a magnetic field ,

The angle through which the pointer on a galvanometer rotates is

Use the diagram for the next problem. -A circular current loop lies in the xy plane and has radius R = 10 cm.The loop has 20 turns and carries a current I = 4 A.The magnetic dipole of the loop is

A beam of electrons moving at a speed of 8 ×\times× 104 m/s is undeflected when it passes through an electric field of 5 N/C perpendicular to its path and a magnetic field that is perpendicular to its path and also to that of the electric field.Calculate the strength of the magnetic field.

A compass needle is in a homogeneous magnetic field with its south pole pointing in the positive direction of .The net force on the compass needle is

In a mass spectrometer ions of Ni with mass 9.62 $\times$ 10^-26 kg and charge +2e are accelerated through a potential difference of X volts and then deflected in a magnetic field of 0.15 T.If the radius of curvature of the ions is 0.55 m,then calculate the value of the potential difference X.

A beam of charged particles moving with a speed of 10⁶ m/s enters a uniform magnetic field of 0.1 T at right angles to the direction of motion.If the particles move in a radius of 0.2 m,then calculate their period of motion.

A beam of electrons moving at a speed of 8 $\times$ 10⁴ m/s is undeflected when it passes through an electric field of 5 N/C perpendicular to its path and a magnetic field that is perpendicular to its path and also to that of the electric field.Calculate the strength of the magnetic field.