Team Quanta gladly presents all possible short questions of Electricity & Magnetism – I’s Chapter#05: Magnetic Field.
Q.1 What is value of and for points inside a current loop?
Answer:
$$\vec{\nabla}.\vec{B}=0$$
$$\vec{\nabla}\times\vec{B}=\mu_0\vec{J}$$
Q.2 Can the path of integration around which we apply Ampere’s law pass through a conductor?
Answer: Yes, the path of integration around which we apply Ampere’s law (Amperian loop) can pass through the conductor.
Q.3 Why ferromagnetism is found in solids only and not in fluid?
Answer: Ferromagnetism is found only in solids because it is due to formation of domains consisting of a group of atomic dipoles. In solids each atomic dipole is very strongly coupled to the neighboring atoms by a quantum mechanical interaction called exchange interaction. This interaction occurs between those atoms which are very close to each other as in solids. In liquids and gases, distance between atoms is large as compared to solids due to which ferromagnetism does not occur in fluids.
Q.4 What is force experienced by a stationary charge in an electric field and a magnetic field?
Answer: The force experienced by a stationary charged particle in electric and magnetic field is called Lorentz force.
$$\vec{F}=q\vec{E}+q\left(\vec{V}\times\vec{B}\right)$$
Q.5 What is angle between direction of flow of current and external magnetic field to have magnetic force of maximum value?
Answer: The force on the current carrying conductor is maximum when the direction of current flow is perpendicular to the direction of external magnetic field.
$$F=ILB\sin{\theta}$$
At $\theta=90o$ , the force on the current carrying conductor is at its maximum value.
Q.6 Is any work done by a magnetic field on a moving charge? Give reasons.
Answer: There is no work done by the magnetic field on moving charge. This is because magnetic force is a conservative force.
Q.7 Give a comparison of electrostatic and magnetic fields.
Answer:
| Electric field | Magnetic field |
| Electric field is created around a charged object.Electric field is defined as the electrostatic force applied on a unit positive charge.It is measured in newton per coulomb. | Magnetic field is created around a moving charge.Magnetic field is proportional to the current flowing through any wire.It is measured in Tesla. |
Q.8 Can a current carrying coil be used as a compass? Explain.
Answer: Yes, the current carrying coil can be used as a compass because of the magnetic poles on its opposite ends.
Q.9 Show that 1 Wb =108.
Answer: Maxwell (Mx) is the unit of magnetic flux in CGS units’ system. In base units
$$1\ Mx=1\ guass\times cm^2$$
As, $1\ guass={10}^{-4}\ T$ and $1\ cm^2={10}^{-4}m^2$
$$1\ Mx={10}^{-4}\ T\times{10}^{-4}m^2$$
$$1\ Mx={10}^{-8}\ Tm^2$$
$$1\ Mx={10}^{-8}\ Wb$$
Q.10 What is the causes of induced emf? From where does this electrical energy come?
Answer: The induced emf is caused when external work done on its source. The external non-electrical energy is converted to electrical energy causing the current flow. This obeys Lenz law and Faraday’s law of electromagnetic induction.
Q.11 A circular loop of wire lies on the floor of the room in which you are sitting. It carries a constant current in a clockwise sense, viewed from above. What is thedirection of the magnetic dipole moment of this current loop?
Answer: By right hand rule, direction of magnetic dipole moment of this current loop is towards floor of room.
Q.12 Wires that carry equal and opposite currents are often twisted together to reduce their magnetic effect at distant points. Why is this effective?
Answer: Since back emf is not produced due to which original resistance is unaffected, so itis effective to twist the wires that carry equal and opposite currents.
Q.13 Why do not we simply define direction of magnetic field B to be direction of magnetic force that acts on a moving charge?
Answer: Magnetic force acting on a moving charge is given by $F=q(\vec{V}\times\vec{B}$ this equation shows that magnetic force is perpendicular to plane containing & anddirection of magnetic field is not direction of magnetic force.
Q.14 Is it meaningful to say that atom is ferromagnetic?
Answer: Ferromagnetism is a macroscopic phenomenon due to formation of domains which consist of a group of large number of atomic dipoles held together by forces of exchange interaction. Thus, a single atom cannot be ferromagnetic. It can only be paramagnetic or diamagnetic.
Q.15 What is angle between direction of flow of current and external magnetic field to have magnetic force of maximum value?
Answer: Magnetic force acting on a current carrying conductor is given by, $F\ =\ ilB\sin{\theta}$. For maximum value of magnetic force, angle between direction of flow of current and external magnetic field should be 90o.
Q.16 A current is sent through a vertical spring, whose lower end weight is hanging. What will happen?
Answer: When a current is sent through a vertical spring from whose lower end weight is hanging, spring begins to oscillate because magnetic field is produced due to flow of current in spring.
Q.17 If a moving electron is deflected sideways in passing through a certain region of space, can we be sure that a magnetic field exists in that region?
Answer: An electron may be deflected by electric or magnetic field. Therefore, if a moving electron is deflected sideways in passing through a certain region of space, we are not sure that a magnetic field exists in that region because there may be electric field and no magnetic field.
Q.18 Is magnetic force conservative or non-conservative. Could we define magnetic potential energy as we defined electric or gravitational potential energy?
Answer: The magnetic force is conservative. Yes, we can define a magnetic potential energy as we defined electric or gravitational potential energy.
Q.19 How could you rule out that the forces between two magnets are electrostatic forces?
Answer: The origin of magnetism is due to motion of electrons in orbits of atoms. These are moving charges. Hence forces between two magnets are not electrostatics.
Q.20 Imagine you arc sitting in a room with your back to one wall. and that an electron beam traveling horizontally from ‘back wall to the front wall is deflected to your right. What is the direction of the uniform magnetic field that exists in the room?
Answer: According to right hand rule, the magnetic field is directed from top of room towards floor of the room.
Q.21 A current carrying loop suspended freely in a magnetic field will rotate to occupy the position of maximum magnetic flux. Explain.
Answer: Torque on a current loop is given by,
$$\tau=NiAB\sin{\theta}$$
When , torque is maximum and magnetic flux linked with loop is zero. Under this torque loop rotates to occupy position with its plane perpendicular to field. In this case θ=0 and $\tau=0$. However, flux linked with loop is a maximum. So, we conclude that a current loop suspended freely in a magnetic field rotates to occupy position of maximum flux.
Q.22 Is energy of a charged particle conserved in magnetic field? How can direction of magnetic force on charge particle be determined?
Answer: Magnetic force on a charged particle always acts at right angle to its direction of motion, it does no work and hence energy of charged particle is conserved in magnetic field. The direction of magnetic force on a charged particle can be determined by three fingers left hand rule called Fleming rule. Stretch thumb, first finger and central finger of left hand so that these are mutually perpendicular. If the first finger points in direction of field, central finger in direction of motion of positive charge (current) then thumb will point in direction of magnetic force.
Q.23 If an electron is not deflected in passing through a certain region of space, can we be sure that there is no magnetic field in that region?
Answer: Magnetic force acting on a charged particle of charge is given by,
$$\vec{F}=q(\vec{v}\times\vec{B})$$
No, if an electron is not deflected in passing through region of space, we are not sure that there is no magnetic field in the region. For example, if electron is moving parallel or anti parallel to magnetic field, there will be no magnetic force acting on electron.
Q.24 Write down formula for magnetic induction at center of a current loop of radius and number of turns . Whether magnetic field is uniform at all points in space?
Answer: Magnetic induction at center of a current loop of radius and number of turns is,
$$B=\frac{\mu_\circ N i}{2R}$$
It is uniform over a small region at its center but non-uniform near the coil walls.
Q.25 Is there any way to set up a magnetic field other than by causing charges to move?
Answer: Magnetic field can be produced by passing a current through a conductor. So there is no other way to set up a magnetic field other than motion of charges.
Q.26 Consider a magnetic field line. Is the magnitude of B constant or variable along such a line?
Answer: According to Biot-Savart law, magnetic field due to a straight conductor varies with distance inversely, so magnitude of magnetic field along a line is variable.
Q.27 What type of magnetic field exists around a current carrying straight conductor?
Answer: Around a current carrying straight conductor, magnetic field exists in form of concentric circles.
Q.28 Does $\vec{F}=i(\vec{l}\times\vec{B})$ hold for a straight wire whose cross-section varies irregularly along its path?
Answer: Since given force is independent of area of cross-section so it holds for a wire whose cross-section varies irregularly.
Q.29 An electron moving along x-axis is acted upon by a magnetic field along y-axis. What is direction of force on it?
Answer: Magnetic force is given by,
$$\vec{F}=q(\vec{v}\times\vec{B})$$
By right hand rule, according to given conditions direction of force will be along z-axis. As electron carries negative charge, direction of force on it is along z-axis
Q.30 A current is sent through a hanging coiled spring. What changes do you expect and why?
Answer: The coiled spring will contract in length as soon as current is passed through it. The coiled spring carrying current is equivalent to series of wires carrying parallel currents in same direction. As two parallel wires carrying currents in same direction attract each other, the coils of spring Come closer together, so the spring contracts in length.
Q.31 A beam of electrons can be deflected either by an electric field or by a magnetic field. Is one method better than the other?
Answer: The deflection of electron beam by electric field is better than deflection of electron beam by magnetic field due to following reasons:
- Electric field is stronger than magnetic field.
- Deflection of electron beam by magnetic field is conditional.
Q.32 Of three vectors in equation $\vec{F}=q(\vec{v}\times\vec{B})$ which pair are always right angles and which may have any angle?
Answer: The pairs $\vec{F}$ & $\vec{v}$ are always at right angle and the pair $\vec{b}$ & $\vec{F}$ may have any angle.
Q.33 The equation $\vec{\tau}=\vec{\mu}\times\vec{B}$ shows that there is no torque on a current loop in an external magnetic field if angle between axis of loop and field is or . What is nature of this equilibrium?
Answer: From given relation,
$$\vec{\tau}=\vec{\mu}\times\vec{B}\ \ \Rightarrow\tau=\left|\vec{\mu}\times\vec{B}\right|=\mu B\sin{\theta}$$
When $\theta=\mathbf{0}$ or $\theta$=180o, then $\tau=0$. This type of equilibrium is called rotational equilibrium.
Q.34 Is uniform for all points within a circular loop of wire carving a current?
Answer: No, is not uniform within a circular loop of wire carrying a current. Thus can be seen by considering the value of magnetic field at a distance from center of loop of radius R is,
$$B=\frac{\mu_\circ i R^2}{2\left(R^2+x^2\right)^{3/2}}$$
However, is uniform at center of loop and is given by,
$$B=\frac{\mu_\circ i R^2}{2R^3}=\frac{\mu_\circ i}{2R}$$
Q.35 What is the cause of induced ? From where does this electrical energy come?
Answer: When a wire loop is moved in a magnetic field, magnetic force pushes the electrons along the wire giving rise to induced current. The direction of this magnetic force is such that it opposes the motion. of loop. The work done in moving loop against this opposing force becomes source of electrical energy in loop.
Q.36 A magnet is moved towards a copper ring. The current induced in the ring will be clockwise or counter clockwise.
Answer: When a magnet is moved towards a copper ring, the current induced in the ring will be counterclockwise
Q.37 A copper ring is placed above a long solenoid with iron core to increase its field. When current is turned on in the solenoid, the copper ring moves upward. Why?
Answer: When current is turned on in solenoid, copper ring moves upward by Lenz law.
Q.38 In which direction are the magnetic lines surrounding a straight wire carrying current that is moving directly toward you?
Answer: The magnetic lines of force will point in counterclockwise direction according to right hand rule.
Q.39 Show that 1 Wb = 108 maxwell.
Answer:
$$1Wb=1T^{{-m}^2}={10}^4G^{{-\left(100cm\right)}^2}={10}^8G^{-cm^2}={10}^8\ mxwell$$
Q.40 What kind of field/fields does/do surround a moving electric charge?
Answer: A charge in constant motion is equivalent to a direct current carrying conductor, it gives rise to a magnetic field represented by magnetic lines of force. These magnetic lines form concentric circles with charge passing through center.
Q.41 If a charged particle moves in a straight line through some region of space, can we say that magnetic field in that region is zero?
Answer: If a charged particle moves in a straight line in a certain region of space; magnetic field may be zero or may be present pointing in direction of motion of charged particle.
Q.42 A hollow copper tube carries a current. Why B=0 inside the tube? Is $B\neq0$ outside the tube?
Answer: The magnetic field produced will circle round the tube. As such B=0 inside the tube and $B\neq0$ outside the tube.
Q.43 Can a current carrying coil be used as a compass? Explain.
Answer: A current carrying coil behaves like a magnet. It will set itself in a particular direction when suspended freely in magnetic field of earth. So, it can be used as compass.
Q.44 A current carrying wire is placed in a magnetic field. How must it be oriented so that force on it is zero?
Answer: Magnetic force is,
$$F=ilB\sin{\theta}$$
When $\theta=0$ , force is zero. Hence it should be placed parallel to magnetic field.
