Derive the torque on a rectangular current-carrying loop placed in a uniform magnetic field. Draw suitable figures. Write one application of this principle.

Let us consider a rectangular loop A B C D is placed in a uniform magnetic field B as shown in the figure. There is a steady current in the loop. Let the width and length of the loop be b and l respectively. The force on arm B C and A D be F A B and F A D respectively. These forces are equal and opposite and act along the axis of the coil. Therefore, these forces will cancel each other out. Similarly, The forces F A B and F C D are also equal and opposite. Since these forces are not colinear, so they act as a couple. Therefore, the magnitude of torque can be given as, τ = F A B b 2 sin θ + F C D b 2 sin θ ∵ F A B = F C D = B I l Therefore, we can say that, τ = B I ( l b ) sin θ Area A = l × b Therefore, τ = B I × A × sin θ We know that, m = I A Therefore, τ = m B sin θ So, the vector form τ → = m → × B → A moving coil galvanometer is the application of this principle.

With the help of a labeled diagram, state the underlying principle of a cyclotron. Explain clearly how it works to accelerate the charged particles. Is there an upper limit on the energy acquired by the particle? Given reason.

Principle: Cyclotron works in this principle that when a charged particle is kept in a magnetic field it experiences a force and the perpendicular magnetic field causes the particle to rotate. Working: A dee which is at a negative potential accelerates the positive ions which are produced from the source S . The magnetic field which is perpendicular will move ions in a circular motion inside the Dees. The magnetic field and the frequency of the applied voltage are so chosen that as the ion comes out of a Dee, the Dees change its polarity(positive becoming negative and vice-versa) and the ion is further accelerated. Now, the ions move with higher velocity along a circular path of greater radius. The phenomenon is continued till the ion reaches the periphery of the Dees where an auxiliary negative electrode )deflecting plate) deflects the accelerated ion on the target to be bombarded. Thus the charged particles accelerate. Yes, there is an upper limit on the energy acquired by the particle because the charged particle gains maximum speed when it moves in a path of radius equal to the radius of Dees. v m a x = q B R m where, R is the radius of Dee. So, the maximum kinetic energy K m a x = 1 2 m v 2 = 1 2 q B R m 2 K m a x = q 2 B 2 R 2 2 m

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The magnetic field at the centre of a circular coil of radius $5 cm$ carrying a current of $1 A$ is $1.256 T$ . If the radius is made $10 cm$ , then the magnetic field at the centre of the loop carrying same current is

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Important Questions on Moving Charges and Magnetism

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 4 - Moving Charges and Magnetism>Meghalaya-2018>Q 5

Calculate the force per unit length between two parallel long straight wires

2 cm

apart in air, each carrying a current of

4 A

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 4 - Moving Charges and Magnetism>Meghalaya-2018>Q 6

Using Biot-Savart law, find an expression for the magnetic field at a point on the axis of a circular current-carrying loop. Hence, find the expression for the magnetic field at its centre.

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12th Meghalaya Board

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 4 - Moving Charges and Magnetism>Meghalaya-2019>Q 7

A charged particle of mass

m

and charge

q

moves along a circular path with a velocity

v

perpendicular to a magnetic field

\vec{B}

. The radius of the circular path is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 4 - Moving Charges and Magnetism>Meghalaya-2019>Q 8

To convert a galvanometer into a voltmeter, we must connect a

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 4 - Moving Charges and Magnetism>Meghalaya-2019>Q 9

Two parallel wires carrying current in the same direction attract each other while two beams of electrons travelling in the same direction repel each other. Explain why.

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 4 - Moving Charges and Magnetism>Meghalaya-2019>Q 10

The wire loop $P Q R S P$ formed by joining two semi-circular wires of radii $R_{1}$ and $R_{2}$ carries a current $I$ as shown in the figure below. Find the magnitude of magnetic field at $O$ .

Question Image

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 4 - Moving Charges and Magnetism>Meghalaya-2019>Q 11

Describe the principle and working of a moving coil galvanometer and hence show that the deflection of the coil is directly proportional to the current flowing through it. What is the effect of the radial magnetic field in a moving coil galvanometer?

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 4 - Moving Charges and Magnetism>Meghalaya-2020>Q 12

What is the relation between current and magnetic moment of a current-carrying circular loop? Use the expression to derive the magnetic dipole moment of a revolving electron.

The magnetic field at the centre of a circular coil of radius 5 cm carrying a current of 1 A is 1.256 T. If the radius is made 10 cm, then the magnetic field at the centre of the loop carrying same current is

Important Questions on Moving Charges and Magnetism

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The magnetic field at the centre of a circular coil of radius $5 cm$ carrying a current of $1 A$ is $1.256 T$ . If the radius is made $10 cm$ , then the magnetic field at the centre of the loop carrying same current is