Question 1

Can we have a single north pole, or a single south pole?

Accepted Answer

No, we cannot have a single north or south pole. Magnetic poles are always found in pairs. They are equal in strength and opposite in nature. Even if we break a magnet into a number of pieces, each piece will become a magnet with equal and opposite poles.

Question 2

Do two distinct poles actually exist at two nearby points in a magnetic dipole?

Accepted Answer

No, two distinct poles cannot exist at two nearby points in a magnet, as a magnet contains only two distinct poles located at its ends.

Question 3

An iron needle is attracted to the ends of a bar magnet but not to the middle region of the magnet. Is the material making up the ends of a bare magnet different from that of the middle  region?

Accepted Answer

No, the material making up the middle region of a magnet is the same as that of the material making up its end. When an iron needle is taken closer to one of the ends of a magnet, the pole of the magnet induces a pole of opposite polarity on the needle, making the needle a magnet itself and thereby making it attracted to that pole.But if we bring the needle closer to the centre of the magnet, then both the poles of the magnet will induce opposite polarity on the needle. As a result, the needle will not get attracted towards the centre of the magnet.

Question 4

Compare the direction of the magnetic field inside a solenoid with that of the field there if the solenoid is replaced by its equivalent combination of north pole and south pole.

Accepted Answer

The direction of the magnetic field is the same in both cases, that is, inside a solenoid and inside a bar magnet. In a solenoid, magnetic field lines are directed from one end to the other internally and externally, so they are in the equivalent combination of north and south poles (as shown in figure).

Question 5

Sketch the magnetic field lines for a current-carrying circular loop near its centre. Replace the loop by an equivalent magnetic dipole and sketch the magnetic field lines near the centre of the dipole. Identify the difference.

Accepted Answer

The difference between the two configurations is that in the current-carrying loop, the magnetic field lines pass through the centre and are perpendicular to its axis; whereas in the equivalent magnetic dipole, the magnetic field lines do not pass through the centre.

Question 6

The force on a north pole, F=mB  , parallel to the field B . Does it contradict our earlier knowledge that a magnetic field can exert forces only perpendicular to itself?

Accepted Answer

Yes, it seems to contradict with our earlier knowledge that a magnetic field can exert forces only perpendicular to itself. F=mBhere , B  = Magnetic fieldm = Magnetic chargEFor a positive magnetic charge, force is along the magnetic field.For a negative magnetic charge, force is opposite to the magnetic field.Thus, it contradicts the notion that a magnetic field can exert forces only perpendicular to itself.

Question 7

Two bar magnets are placed close to each other with their opposite poles facing each other. In absence of other forces, the magnets are pulled towards each other and their kinetic energy increases. Does it contradict our earlier knowledge that magnetic forces cannot do any work and hence cannot increase kinetic energy of a system?

Accepted Answer

Yes, it contradicts our earlier knowledge that magnetic forces cannot do any work and hence cannot increase the kinetic energy of the system. When opposite poles are facing each other, an attractive force acts between them so the magnets are pulled towards each other. As the two magnets come close to each other so the force between them increases and hence, the kinetic energy also increases.

Question 8

Magnetic scalar potential is defined as U(r2​​)−U(r1​​)=−∫r1​r2​​B⋅dl Apply this equation to a closed curve enclosing a long straight wire. The RHS of the above equation is then −μ0​i by Ampere's law. We see that U(r2​​)=U(r1​​)  even when r2​​=r1​​. Can we have a magnetic scalar potential in this case?

Accepted Answer

No, we cannot have a magnetic scalar potential here.Ampere's law is a method of calculating magnetic field due to current distribution. On the other hand, magnetic scalar potential requires a magnetic field due to pole strength m.Potential at a distance r is given by 4πrμ0​m​ As there is no current distribution, no magnetic field due to poles or the pole strength is present. That is why we cannot have a magnetic scalar potential in this case.

Question 9

Can the earth's magnetic field be vertical at a place? What will happen to a freely suspended magnet at such a place? What is the value of dip here?

Accepted Answer

Yes, Earth's magnetic field is vertical at the poles. A freely suspended magnet becomes vertical at the poles, with its north pole pointing towards Earth's north pole, which is magnetic south.The value of the angle of the dip here is 90°.

Question 10

Can the dip at a place be (a) zero (b) 90°?

Accepted Answer

(a) Yes, the dip can be zero at the equator of Earth.(b) Yes, the dip can be 90°​ at the poles of Earth.

Question 11

The reduction factor K of a tangent galvanometer is written on the instrument. The manual says that the current is obtained by multiplying this factor to tan θ. The procedure works well at Bhuwaneshwar. Will the procedure work if the instrument is taken to Nepal? If there is same error, can it be corrected by correcting the manual or the instrument will have to be taken back to the factory?

Accepted Answer

Yes, the procedure will work if the instrument is taken to Nepal, as the current at a place can be calculated by multiplying the reduction factor K with tan θ of that place . In our case, we will take the value of tan θ of Nepal, as tan θ may vary from place to place. tan θ at any place is determined from the mathematical formula BH​B​, where B is the external magnetic field and BH​ is the horizontal component of Earth's magnetic field Thus, we need not take the manual or the instrument back to the factory for correction.

Question 12

A circular loop carrying a current is replaced by an equivalent magnetic dipole. A point on the axis of the loop is in:

Accepted Answer

End-on positionPoints lying on the axis of a magnet are called end-on points. In our case, the point on the axis of the loop (on replacing the circular loop with an equivalent magnetic dipole) lies on the axis of the magnetic dipole or on the end-on position.If P was the point on the axis of the loop, then it is clear from the figure that P lies on the end-on position of the equivalent magnetic dipole.

Question 13

A circular loop carrying a current is replaced by an equivalent magnetic dipole. A point on the loop is in:

Accepted Answer

Broadside-on positionThe position of the points lying on the equator of a magnetic dipole is called the broadside-on position. In our case, the point on the loop (after replacement of the circular loop with an equivalent magnetic dipole) lies on the equatorial position of the equivalent magnetic dipole. Hence, the point lies on the broadside-on position.If P was the point on the loop, then it is clear from the figure that point P lies on the broadside-on position of the equivalent magnetic dipole.

Question 14

When a current in a circular loop is equivalently replaced by a magnetic dipole,

Accepted Answer

The product md is fixedWhen we replace a circular current-carrying loop with a magnetic dipole to resemble field lines of the circular loop, the pole strength m and the distance between the poles are not fixed.But the magnetic dipole moment of both systems is always fixed. It is the product of the magnetic moment and the distance between the poles. In other words, md is fixed.A current loop of area A and current I can be replaced with a magnetic dipole of dipole moment md.i.e. md=IA

Question 15

Let r be the distance of a point on the axis of a bar magnet from its centre. The magnetic field at such a point is proportional to:

Accepted Answer

Magnetic field B due to a bar magnet of magnetic moment M at distance r of the point on the axis of the magnet from its centre is given byB=4πμo​​(r2−l2)22Mr​ Here, 2l  is the length of the magnet.So, from the above formula, it can be easily seen that B∝(r2−l2)2r​

Question 16

Let r be the distance of a point on the axis of a magnetic dipole from its centre. The magnetic field at such a point is proportional to:

Accepted Answer

Magnetic field B due to a bar magnet of magnetic moment M at distance r of the point on the axis from its centre is given by B=4π(r2−l2)2μ0​2Mr​ Here, 2l  is the length of the magnet.When the distance of the point where the magnetic field has to be calculated is greater than the length of the magnet, i.e r>>l , the bar magnet acts like a magnetic dipole whose magnetic field is B∝r31​ Now, l  in the denominator can be neglected.So, the correct option is (c).

Question 17

Two short magnets of equal dipole moments M are fastened perpendicularly at their centre in the Figure . The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is:

Accepted Answer

Magnetic field (B1​) due to the short dipole A of dipole moment M at an axial point is given by,B1​=4πμ0​​d32M​…(1) Magnetic field (B2​) due to the short dipole B of dipole moment M at an axial point is given by,B2​=4πμ0​​d32M​…(2) Resultant magnetic field (B) will be,B=B12​+B22​​B=4πμ0​​d322​M​​

Question 18

Magnetic meridian is:

Accepted Answer

Magnetic meridian at a place is not a line but a vertical plane passing through the axis of a freely suspended magnet.

Question 19

A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It:

Accepted Answer

When taken to a geomagnetic pole, a compass needle that is allowed to move in a horizontal plane will try to suspend itself vertically to the horizontal plane containing the compass. In other words, the horizontal plane containing the compass will restrict the compass to suspend itself in vertical direction; hence, the compass will stay in any position.However, a freely suspended magnet will become vertical at poles, with its north pole pointing towards Earth at its north pole (which is magnetic south).

Question 20

A dip circle is taken to geomagnetic equator. The needle is allowed to move in a vertical plane perpendicular to the magnetic meridian. The needle will stay:

Accepted Answer

in the direction it is releasedAt the geomagnetic equator, the needle tries to suspend itself in horizontal direction. But here the needle is restricted to move only in the vertical plane perpendicular to the magnetic meridian. Hence, the needle will stay in the direction it is released.

Chapter 14 : Permanent Magnets