Do magnetic forces obey Newton’s third law. Verify for two current elements d l 1 = d l i ^ located at the origin and d l 2 = d l j ^ located at ( 0 , R , 0 ) . Both carry current I .

Suppose two current elements d l 1 and d l 2 located at ( 0 , 0 , 0 ) and ( 0 , R , 0 ) . The direction of magnetic field on d l 2 due to magnetic field B 1 produced by d l 1 will be along towards z-axis (by using Right Hand thumb rule). Since, l 2 ⊥ B 1 . Then force on d l 2 due to magnetic field B 1 : F 21 = I 2 d l 2 × B 1 = B 1 I 2 d l 2 sin 90 ° = B 1 I 2 d l 2 The force on d l 1 due to magnetic field B 2 is none because B 2 ∥ d l 1 i.e. F 12 = I 1 d l 1 × B 2 = B 2 I 1 d l 1 sin 0 ° = 0 Thus, F 12 ≠ F 21 . Hence, it doesn't follow Newtons third law of motion.

An electron and a positron are released from ( 0 , 0 , 0 ) and ( 0 , 0 , 1 . 5 R ) respectively, in a uniform magnetic field B = B ∘ i ^ , each with an equal momentum of magnitude p = e B R . Under what conditions on the direction of momentum will the orbits be non-intersecting circles?

Here, B = B ∘ i ^ i.e. magnetic field is along x-axis. So, for the circular motion both electron and positron, their momenta must be in y-z plane. Suppose, p 1 and p 2 are the momentum of the electron and positron, respectively. Both particle traverse a circular path of radius R but in opposite direction. Suppose both particles make an angle θ with y-axis. The centres of the respective circles must be perpendicular to the momenta and at a distance R . Let the centre of the electron be at C e and of the positron at C p . Coordinates of C e is 0 , - R sin θ , R cos θ Coordinates of C p is 0 , - R sin θ , 1 . 5 R - R cos θ If the distance between the two centres is more than 2 R then they will not overlap. Suppose, d is the distance between C e and C p Then, d 2 = R sin θ - - R sin θ 2 + R cos θ - 3 2 R - R cos θ 2 ⇒ d 2 = ( 2 R sin θ ) 2 + 2 R co s θ - 3 2 R 2 ⇒ d 2 = 4 R 2 sin 2 θ + 4 R 2 co s 2 θ + 3 2 2 R 2 - 6 R 2 cos θ ⇒ d 2 = 4 R 2 sin 2 θ + cos 2 θ + 9 4 R 2 - 6 R 2 cos θ ⇒ d 2 = 4 R 2 + 9 4 R 2 - 6 R 2 cos θ Since, d > 2 R then d 2 > 4 R 2 So, 4 R 2 + 9 4 R 2 - 6 R 2 cos θ > 4 R 2 ⇒ 9 4 R 2 > 6 R 2 cos θ ⇒ 9 4 > 6 cos θ ⇒ cos θ < 3 8 ⇒ θ = cos - 1 3 8 The angle made by momenta of both electron and positron should be less than cos - 1 3 8 so that orbits remain non-intersecting.

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A charged particle of charge $e$ and mass $m$ is moving in an electric field $E$ and magnetic field $B$ . Construct dimensionless quantities and quantities of dimension $[T]^{- 1}$ .

Important Questions on Moving Charges and Magnetism

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NCERT Exemplar Physics - Class 12>Chapter 4 - Moving Charges and Magnetism>SA>Q 4.19

An electron enters with a velocity

v = ν_{\circ} i

into a cubical region (faces parallel to coordinate planes) in which there are uniform electric and magnetic fields. The orbit of the electron is found to spiral down inside the cube in plane parallel to the x-y plane. Suggest a configuration of fields

E

and

B

that can lead to it.

MEDIUM

12th CBSE

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NCERT Exemplar Physics - Class 12>Chapter 4 - Moving Charges and Magnetism>SA>Q 4.2

Do magnetic forces obey Newton’s third law. Verify for two current elements

d l_{1} = d l \hat{i}

located at the origin and

d l_{2} = d l \hat{j}

located at

(0, R, 0)

. Both carry current

I

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NCERT Exemplar Physics - Class 12>Chapter 4 - Moving Charges and Magnetism>SA>Q 4.21

A multirange voltmeter can be constructed by using a galvanometer circuit, as shown in figure. We want to construct a voltmeter that can measure $2 V$ , $20 V$ and $200 V$ using a galvanometer of resistance $10 Ω$ and that produces maximum deflection for current of $1 mA$ . Find $R_{1}$ , $R_{2}$ and $R_{3}$ that have to be used.

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NCERT Exemplar Physics - Class 12>Chapter 4 - Moving Charges and Magnetism>SA>Q 4.22

A long straight wire carrying current of $25 A$ rests on a table as shown in figure. Another wire $P Q$ of length $1 m$ , mass $2.5 g$ carries the same current but in the opposite direction. The wire $P Q$ is free to slide up and down. To what height will $P Q$ rise?

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NCERT Exemplar Physics - Class 12>Chapter 4 - Moving Charges and Magnetism>LA>Q 4.23

A $100$ turn rectangular coil $ABCD$ (in $XY$ plane) is hung from one arm of a balance (Fig). A mass $500 g$ is added to the other arm to balance the weight of the coil. A current $4.9 A$ passes through the coil and a constant magnetic field of $0.2 T$ acting inward (in xz plane) is switched on such that only arm $CD$ of length $1 cm$ lies in the field. How much additional mass $‘ m ’$ must be added to regain the balance?

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NCERT Exemplar Physics - Class 12>Chapter 4 - Moving Charges and Magnetism>LA>Q 4.24

A rectangular conducting loop consists of two wires on two opposite sides of length

l

joined together by rods of length

d

The wires are each of the same material but with cross-sections differing by a factor of

2

. The thicker wire has a resistance

R

and the rods are of low resistance, which in turn are connected to a constant voltage source

V_{0}

. The loop is placed in uniform a magnetic field

B

45 °

to its plane. Find

τ

, the torque exerted by the magnetic field on the loop about an axis through the centres of rods.

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NCERT Exemplar Physics - Class 12>Chapter 4 - Moving Charges and Magnetism>LA>Q 4.25

An electron and a positron are released from

(0, 0, 0)

and

(0, 0, 1.5 R)

respectively, in a uniform magnetic field

B = B_{\circ} \hat{i}

, each with an equal momentum of magnitude

p = e B R

. Under what conditions on the direction of momentum will the orbits be non-intersecting circles?

HARD

12th CBSE

IMPORTANT

NCERT Exemplar Physics - Class 12>Chapter 4 - Moving Charges and Magnetism>LA>Q 4.26

A uniform conducting wire of length

12 a

and resistance

R

is wound up as a current carrying coil in the shape of (i) an equilateral triangle of side

a

, (ii) a square of sides

a

and, (iii) a regular hexagon of sides

a

The coil is connected to a voltage source

V_{0}

. Find the magnetic moment of the coils in each case.

A charged particle of charge e and mass m is moving in an electric field E and magnetic field B. Construct dimensionless quantities and quantities of dimension [T]-1.

Important Questions on Moving Charges and Magnetism

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A charged particle of charge $e$ and mass $m$ is moving in an electric field $E$ and magnetic field $B$ . Construct dimensionless quantities and quantities of dimension $[T]^{- 1}$ .