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CBSE Class 12 NCERT Physics Moving Charges and Magnetism
Moving Charges and Magnetism

Five long wires A, B, C, D, and E each carrying I are arranged to form edges of a pentagonal prism as shown in the figure. Each carries current out of the plane of paper. a) what will be magnetic induction at a point on the axis O> Axis is at a distance R from each wire b) what will be the field if current in one of the wires is switched off c) what if current in one of the wire A is reversed

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(a) Because A, B, C, D, and E are perpendicular to the plane of paper at the specified places, the magnetic induction at a point on the axis will be zero, which is represented by R. (b) The field...

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A uniform conducting wire of length 12a 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 if sides a and iii) a regular hexagon of sides a. The coil is connected to a voltage source V0. Find the magnetic moment of the coils in each case.

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a) A triangle with side a that is equilateral. Number of loops = 4 A = √3/4 a2 m = Ia2√3 is the magnetic moment. b) In the case of a square with sides of a A = a2 Number of loops = 3 m =...

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An electron and a positron are released from (0, 0, 0) and (0, 0, 1.5R) respectively, in a uniform magnetic field each with an equal momentum of magnitude p = eBR. Under what conditions on the direction of momentum will the orbits be non-intersecting circles?

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The circular orbits of electron and positron should not overlap when the centres are bigger than 2R. Let the distance between Cp and Ce be denoted by d. Then  d2 = 4R2 + 9/4R2 – 6R2 cosθ Because d...

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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 Vo. The loop is placed in uniform a magnetic field B at 45oto 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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F1 = i1l B sin 90o = V0/2R lB τ1= d/2√2 F1 = V0ldB/2√2 R τ = 1/4√2 V0AB/R

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A 100 turn rectangular coil ABCD is hung from one arm of a balance. 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 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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When t = 0, the external magnetic field is off. Mgl = Wcoil l 0.5 gl = Wcoil l Wcoil = 0.5 9.8 N Let m be the mass that is added to restore equilibrium. The magnetic field is activated when the...

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

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The magnetic field produced by a long straight current-carrying wire is given as B = μ0I/2πh Magnetic force on the small conductor is F = BIl sin θ = BIl F = mg = μ0I2l/2πh h = 0.51...

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A multirange voltmeter can be constructed by using a galvanometer circuit as shown in the figure. We want to construct a voltmeter that can measure 2V, 20V, and 200V using galvanometer of resistance 10Ω and that produces maximum deflection for a current of 1 mA. Find R1, R2, and R3 that have to be used.

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iG(G+R1) = 2 for 2V range iG(G+R1+R2) = 20 for 20V range iG(G+R1+R2+R3) = 200 for 200V range Solving the above, we get R1 = 1990 Ω R2 = 18kΩ R3 = 180 kΩ

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Two long wires carrying current $I_{1}$ and $I_{2}$ are arranged as shown in the figure. The one carrying I1 is along is the x-axis. The other carrying current I2 is along a line parallel to the y-axis given by x = 0 and z = d. Find the force exerted at O2 because of the wire along the x-axis.

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F = I(L×B) = ILB sinθ is the magnetic field B on a current-carrying wire. O2 and I1  are in the –Y direction and parallel to the y-axis I2 is perpendicular to the y-axis and parallel to the Y-axis,...

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A cubical region of space is filled with some uniform electric and magnetic fields. An electron enters the cube across one of its faces with velocity v and a positron enters via opposite face with velocity –v. At this instant, a) the electric forces on both the particles cause identical acceleration b) the magnetic forces on both the particles cause equal accelerations c) both particles gain or lose energy at the same rate d) the motion of the centre of mass (CM) is determined by B alone

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b) the magnetic forces on both the particles cause equal accelerations c) both particles gain or lose energy at the same rate d) the motion of the centre of mass (CM) is determined by B alone

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Consider a wire carrying a steady current, I placed un a uniform magnetic field B perpendicular to its length. Consider the charges inside the wire. It is known that magnetic forces do not work. This implies that a) motion of charges inside the conductor is unaffected by B since they do not absorb energy b) some charges inside the wire move to the surface as a result of B c) if the wire moves under the influence of B, no work is done by the force d) if the wire moves under the influence of B, no work is done by the magnetic force on the ions, assumed fixed within the wire

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b) some charges inside the wire move to the surface as a result of B d) if the wire moves under the influence of B, no work is done by the magnetic force on the ions, assumed fixed within the wire

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A uniform magnetic field of $1.5 \mathrm{~T}$ exists in a cylindrical region of a radius of $10.0 \mathrm{~cm}$, its direction parallel to the axis along east to west. A wire carrying a current of $7.0$ A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if, the wire in the N-S direction is lowered from the axis by a distance of $6.0 \mathrm{~cm} ?$

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When the wire is lowered by $6 \mathrm{~cm}$, then Then, $x=\sqrt{(10)^{2}-\left(6^{2}\right)}=\sqrt{64}=8 \mathrm{~cm}$ $2 \mathrm{x}=\mathrm{I}_{2}=16 \mathrm{~cm}$ $F_{2}=BII_{2}$=$1.5 \times 7...

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Answer the following question:
An electron travelling west to east enters a chamber having a uniform electrostatic field in the north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight-line path.

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Because of the electric field, the negatively charged electron tends to go towards the north. The electron will not be deflected if an equal magnetic force acts in the other direction. We derive the...

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A solenoid $60 \mathrm{~cm}$ long and of radius, $4.0 \mathrm{~cm}$ has 3 layers of windings of 300 turns each. A $2.0 \mathrm{~cm}$ long wire of mass $2.5 \mathrm{~g}$ lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of $6.0 \mathrm{~A}$ in the wire. What value of current (with an appropriate sense of circulation) in the windings of the solenoid can support the weight of the wire? $\mathrm{g}=9.8 \mathrm{~m} \mathrm{~s}^{-2}$.

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Length of the solenoid is given as I $=60 \mathrm{~cm}$ Layers of windings is $3$ Each layer has 300 turns Number of turns per unit length, $n=(3 \times 300) / 0.6=1500 \mathrm{~m}^{-1}$ Inside the...

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A circular coil of 20 turns and a radius of $10 \mathrm{~cm}$ is placed in a uniform magnetic field of $0.10 \mathrm{~T}$ normal to the plane of the coil. If the current in the coil is $5.0 \mathrm{~A}$, what is the average force on each electron in the coil due to the magnetic field? (The coil is made of copper wire of cross-sectional area $10^{-5} \mathrm{~m}^{2}$, and the free electron density in copper is given to be about $10^{29} \mathrm{~m}^{-3} .$

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Number of turns is given as $\mathrm{n}=20$ turns Radius of the coil is given as $r=10 \mathrm{~cm}=0.1 \mathrm{~m}$ Current in the coil is given as $I=5 \mathrm{~A}$ Magnetic field strength is...

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A circular coil of 20 turns and a radius of $10 \mathrm{~cm}$ is placed in a uniform magnetic field of $0.10 \mathrm{~T}$ normal to the plane of the coil. If the current in the coil is $5.0 \mathrm{~A}$, what is the (a) total torque on the coil, (b) the total force on the coil,

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Number of turns is given as n = 20 Radius of the coil is given as r = 0.1m Current in the coil is given as $I$ = 5A Magnetic field strength is given as $B$ =0.10 T Cross-sectional area of the wire...

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A uniform magnetic field of $3000 \mathrm{G}$ is established along the positive z-direction. A rectangular loop of sides $10 \mathrm{~cm}$ and $5 \mathrm{~cm}$ carries a current of $12 \mathbf{A} .$ What is the torque on the loop in the different cases shown in the figure? What is the force on each case? Which case corresponds to stable equilibrium?

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(a) We can see from the diagram that A is normal to the x-y plane in the positive z-direction and B is parallel to the z-axis. $\vec{A}=50 \times 10^{-4} \hat{k}$ $\vec{B}=0.3 \hat{k}$ Accordingly,...

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A uniform magnetic field of $3000 \mathrm{G}$ is established along the positive z-direction. A rectangular loop of sides $10 \mathrm{~cm}$ and $5 \mathrm{~cm}$ carries a current of $12 \mathbf{A} .$ What is the torque on the loop in the different cases shown in the figure? What is the force on each case? Which case corresponds to stable equilibrium?

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(a) $B$ is along the z-axis and $A$ is normal to the $x-z$ plane. $\vec{A}=-50 \times 10^{-4} \hat{j}$ $\vec{B}=0.3 \hat{k}$ $\vec{\tau}=12 \times\left(-50 \times 10^{-4}\right) \hat{j} \times 0.3...

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A uniform magnetic field of $3000 \mathrm{G}$ is established along the positive z-direction. A rectangular loop of sides $10 \mathrm{~cm}$ and $5 \mathrm{~cm}$ carries a current of $12 \mathbf{A} .$ What is the torque on the loop in the different cases shown in the figure? What is the force on each case? Which case corresponds to stable equilibrium?

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Magnetic field strength is given as $B=3000 \mathrm{G}=0.3 \mathrm{~T}$Area of the loop will be, $A=10 \times 5=50 \mathrm{~cm}^{2}=50 \times 10^{-4} \mathrm{~m}^{2}$Current flowing in the loop is,...

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A uniform magnetic field of $1.5 \mathrm{~T}$ exists in a cylindrical region of a radius of $10.0 \mathrm{~cm}$, its direction parallel to the axis along east to west. A wire carrying a current of $7.0$ A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if, (a) the wire intersects the axis, (b) the wire is turned from N-S to the northeast-northwest direction

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(a) Magnetic field, $B=1.5 \mathrm{~T}$ Current in the wire, $I=7.0 \mathrm{~A}$ Radius, $r=10 \mathrm{~cm}=0.1 \mathrm{~m}$ Diameter, $\mid=2 \times r=0.2 \mathrm{~m}$ On the wire, a force $2.1...

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The wires which connect the battery of an automobile to its starting motor carry a current of $300 \mathrm{~A}$ (for a short time). What is the force per unit length between the wires if they are $70 \mathrm{~cm}$ long and $1.5 \mathrm{~cm}$ apart? Is the force attractive or repulsive?

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Current flowing in the wires, $\mid=300 \mathrm{~A}$ Wires are separated by distance, $d=1.5 \mathrm{~cm}=0.015 \mathrm{~m}$ Length of the wires, $\mid=70 \mathrm{~cm}=0.7 \mathrm{~m}$ Force between...

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A straight horizontal conducting rod of length $0.45 \mathrm{~m}$ and mass $60 \mathrm{~g}$ is suspended by two vertical wires at its ends. A current of $5.0 \mathrm{~A}$ is set up in the rod through the wires. (a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?(b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field the same as before? (Ignore the mass of the wires.) $\mathbf{g}=9.8 \mathrm{~m} \mathrm{~s}^{-2}$.

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Length of the rod, I $=0.45 \mathrm{~m}$ Mass suspended, $m=60 \mathrm{~g}=60 \times 10^{-3} \mathrm{Kg}$ Current, $\mid=5 \mathrm{~A}$ (a) Tension in the wire is zero if the magnetic field's force...

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A magnetic field set up using Helmholtz coils (described in Exercise $4.16$ ) is uniform in a small region and has a magnitude of $0.75 \mathrm{~T}$. In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through $15 \mathrm{kV}$ enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is $9.0 \times 10^{-5} \mathrm{~V} \mathrm{~m}^{-1}$, make a simple guess as to what the beam contains. Why is the answer not unique?

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Magnetic field, $B=0.75 \mathrm{~T}$ Accelerating voltage, $\mathrm{V}=15 \mathrm{kV}=15 \times 10^{3} \mathrm{~V}$ Electrostatic field, $E=9.0 \times 10^{-5} \mathrm{~V} \mathrm{~m}^{-1}$ Kinetic...

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An electron emitted by a heated cathode and accelerated through a potential difference of $2.0 \mathrm{kV}$, enters a region with a uniform magnetic field of $0.15 \mathrm{~T}$. Determine the trajectory of the electron if the field (a) is transverse to its initial velocity, (b) makes an angle of $30^{\circ}$ with the initial velocity.

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Magnetic field, $B=0.15 \mathrm{~T}$ Potential difference, $\mathrm{V}=2.0 \mathrm{kV}$ An electron obtains kinetic energy as a result of $\mathrm{E}=(1 / 2) \mathrm{mv}^{2}$ $\mathrm{eV}=(1 / 2)...

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Answer the following questions: (a) A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle? (b) A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?

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(a) The force acting on a charged particle, moving in a magnetic field is given by F = q v B sinθ  now, if no force acts on the charged particle, it will proceed along a straight path at a constant...

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For a circular coil of radius $\mathrm{R}$ and $\mathrm{N}$ turns carrying current $\mathrm{I}$, the magnitude of the magnetic field at a point on its axis at a distance $x$ from its centre is given by, $B=\frac{\mu_{0} I R^{2} N}{2\left(x^{2}+R^{2}\right)^{3 / 2}}$ (a) Show that this reduces to the familiar result for field at the centre of the coil. (b) Consider two parallel co-axial circular coils of equal radius $\mathbf{R}$, and number of turns $\mathbf{N}$, carrying equal currents in the same direction, and separated by a distance $\mathbf{R} .$ Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to $\mathbf{R}$, and is given by, $B=0.72 \frac{\mu_{0} N I}{R}$, approximately.

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(a) Given is the expression of $B$ as $\frac{\mu_{0} I R^{2} N}{2\left(x^{2}+R^{2}\right)^{3 / 2}}$ $x$ will be zero at the centre of the coil, Therefore, the magnetic field at the centre is...

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(a) A circular coil having radius as 8.0 cm, number of turn as 30 and carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an angle of $60^{o}$ with the normal of the coil. To prevent the coil from turning, determine the magnitude of the counter-torque that must be applied. (b) Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)

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(a) Number of turns on the circular coil (n) is given as 30 Radius of the coil (r) is given as 0.08 m Area of the coil: $\pi {r^2}$= $\pi {(0.08)^2}$= $0.0201{m^2}$ Current flowing in the coil (I) =...

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A toroid has a core (non-ferromagnetic) of inner radius $25 \mathrm{~cm}$ and outer radius $26 \mathrm{~cm}$, around which 3500 turns of a wire are wound. If the current in the wire is $11 \mathrm{~A}$, what is the magnetic field?(a) outside the toroid, (b) inside the core of the toroid

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The core's inner radius, $r_{1}=0.25 \mathrm{~m}$ The core's outer radius, $r_{2}=0.26 \mathrm{~m}$ The number of wire turns, $N=3500$ turns Current in the wire, $1=11 \mathrm{~A}$ (a) Outside of...

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A magnetic field of 100 G is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about ${{10}^{-3}}$ m2. The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound around a core is at most 1000 turns ${{m}^{-1}}$. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

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Magnetic field strength, B is given as $100 \times {10^{-4}}T$ Number of turns per unit length, N is given as 1000 turns/m Current carrying capacity of the coil is given as 15 A Permeability of free...

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Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

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Radius of the coil X, r1 is given as 0.16 m Number of turns in coil X, n1 is given as 20 Current in the coil X, I1 is given as 16 A Radius of the coil Y, r2 is given as 0.1 m...

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In a chamber, a uniform magnetic field of 6.5 G is maintained. An electron is shot into the field with a speed of 4.8 x $10^{6}$ m$s^{-1}$ normal to the field. Find the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

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Given, Magnetic field strength (B) = 6.5 G = $6.5 \times {10^{ - 4}}T$ Speed of the electron (v) = $4.8 \times {10^6}m/s$ Charge on the electron (e) = $1.6 \times {10^{ - 19}}C$ Mass of the electron...

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In a chamber, a uniform magnetic field of 6.5 G (1 G = $10^{-4}$ T) is maintained. An electron is shot into the field with a speed of $4.8 \times {10^6}m/s$ normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit.

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Magnetic field strength (B) = 6.5 G = $6.5 \times {10^{ - 4}}T$ Speed of the electron (v) = $4.8 \times {10^6}m/s$ Charge on the electron (e) = $1.6 \times {10^{ - 19}}C$ Mass of the electron (me)...

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A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30º with the direction of a uniform
the horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?

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The length of a square coil's side (l) is 0.1 m. The current flowing through the coil (I) has a magnitude of 12 A. The number of coil turns (n) is 20. The angle formed by the coil's plane with B...

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