Q: Derive an expression for magnetic field at a point on the axial line of a bar magnet.

Let \$NS\$ be a bar magnet of magnetic length \$2l\$ and having each pole of magnetic strength \$m\$ . O is the center of magnet and \$P\$ is a point on axial line at a distance \$r\$ from the center \$O\$ of magnet , at which magnetic field has to be measured .The magnetic field \$B_{1}\$ at \$P\$ due to \$N\$ pole of magnet , \$B_{1}=\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{NP^{2}}\$or \$B_{1}=\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{(r-l)^{2}}\$ (along PX) .......................eq1And , the magnetic field \$B_{2}\$ at \$P\$ due to \$S\$ pole of magnet , \$B_{2}=\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{SP^{2}}\$or \$B_{2}=\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{(r+l)^{2}}\$ (along PS) ......................eq2Therefore , resultant magnetic field at point \$P\$ , \$B=B_{1}-B_{2}\$ (-ive sign is due to opposite directionS of \$B_{1}\$ and \$B_{2}\$)It is clear from eq1 and eq2 that \$B_{1}>B_{2}\$ ,therefore the direction of \$B\$ will be along \$PX\$ .or \$B=\$\$\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{(r-l)^{2}}\$\$-\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{(r+l)^{2}}\$ (alongPX)or \$B=\dfrac{\mu_{0}}{4\pi}.\dfrac{m(4rl)}{(r^{2}-l^{2})^{2}}\$ (alongPX)Now , \$m(2l)=M\$ (magnetic dipole moment of magnet)Hence , \$B=\dfrac{\mu_{0}}{4\pi}.\dfrac{2Mr}{(r^{2}-l^{2})^{2}}\$ (alongPX)

Q: \$F_g\$ and \$F_e\$ represent gravitational and electrostatic force respectively between electrons situated at a distance \$0.1\,m. F_g/F_e\$ is of the order

\${ F }_{ y }\$ and \${ F }_{ e }\$ represent gravitational and electrostatic force respectively between electrons situated at a distance \$=0.1m\$let, us take the ratio\$\dfrac { { F }_{ e } }{ { F }_{ g } } =\dfrac { \dfrac { 1 }{ 4\pi { \epsilon }_{ 0 } } \dfrac { { q }^{ 2 } }{ { d }^{ 2 } } }{ G\dfrac { { m }^{ 2 } }{ { d }^{ 2 } } } \$\$\dfrac { { F }_{ e } }{ { F }_{ g } } =\dfrac { 1 }{ 4\pi { \epsilon }_{ 0 } } \times \dfrac { 1 }{ G } \times \dfrac { { q }^{ 2 } }{ { m }^{ 2 } } \$\$\dfrac { { F }_{ e } }{ { F }_{ g } } =9\times { 10 }^{ 9 }\times \dfrac { 1 }{ 6.67\times { 10 }^{ -11 } } \times \dfrac { { \left( 1.6\times { 10 }^{ -19 } \right) }^{ 2 } }{ { \left( 9.1\times { 10 }^{ -31 } \right) }^{ 2 } } \$\$\Rightarrow \dfrac { { F }_{ e } }{ { F }_{ g } } =4.17\times { 10 }^{ 42 }\$or, \$\dfrac { { F }_{ e } }{ { F }_{ g } } \$ is of the order of \${ 10 }^{ -42 }\$.

Q: The ratio of magnitude of electrostatic force and gravitational force for an electron and proton is

Here, for an electron and a protonElectrostatic force, \$\left| { F }_{ e } \right| =\cfrac { 1 }{ 4\pi { \varepsilon }_{ 0 } } \cfrac { { e }^{ 2 } }{ { r }^{ 2 } } \$Gravitational force, \$\left| { F }_{ g } \right| =\cfrac { G{ m }_{ e }{ m }_{ p } }{ { r }^{ 2 } } \$\$\therefore \cfrac { \left| { F }_{ e } \right| }{ \left| { F }_{ g } \right| } =\cfrac { 1 }{ 4\pi { \varepsilon }_{ 0 } } \cfrac { { e }^{ 2 } }{ G{ m }_{ e }{ m } } =\cfrac { 9\times { 10 }^{ 9 }\times { \left( 1.6\times { 10 }^{ -19 } \right) }^{ 2 } }{ 6.67\times { 10 }^{ -11 }\times 9\times { 10 }^{ -31 }\times 1.66\times { 10 }^{ -27 } } =2.4\times { 10 }^{ 39 }\$

Q: The ratio of electric force to the gravitational force between two protons separated by a finite distance is of the order of:

\$Gravitational\ force\ = \dfrac{G(m_p)^2}{r^2}\$\$Electric\ force\ = \dfrac{K(e)(e)}{r^2}\$\$Ratio\ = \dfrac{K(1.6\times 10^{-19})^2}{r^2}\times \dfrac{r^2}{G\times (1.6\ 7\times 10^{-27})^2}\$\$= \dfrac{(9\times 10^9)\times (1.6\times 10^{-19})^2}{(6.6\ 7\times 10^{-11})(1.6\ 7\times 10^{-27})^2}\$\$=1.23\times 10^{20}\times 10^{16}\$\$= 10^{36}\$(order of magnitude)

Question 1

Why do magnetic field lines not intersect each other?

Accepted Answer

If magnetic field lines intersect each other, then at the intersection point there will be two directions of the same field which is not possible. Hence the field lines do not cross or intersect each other.

Question 2

The magnetic field in a given region is uniform. Draw a diagram to represent it.

Accepted Answer

Uniform magnetic field is  represented by  parallel magnetic field lines  in same direction.

Question 3

Derive an expression for magnetic field at a point on the axial line of a bar magnet.

Accepted Answer

Let $NS$ be a bar magnet of magnetic length $2l$ and having each pole of magnetic strength $m$ . O is the center of magnet and $P$ is a point on axial line at a distance $r$ from the center $O$ of magnet , at which magnetic field has to be measured .The magnetic field $B_{1}$ at $P$ due to $N$ pole of magnet ,      $B_{1}=\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{NP^{2}}$or   $B_{1}=\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{(r-l)^{2}}$   (along PX) .......................eq1And , the magnetic field $B_{2}$ at $P$ due to $S$ pole of magnet ,      $B_{2}=\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{SP^{2}}$or   $B_{2}=\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{(r+l)^{2}}$   (along PS) ......................eq2Therefore , resultant magnetic field at point $P$ ,       $B=B_{1}-B_{2}$  (-ive sign is due to opposite directionS of $B_{1}$ and $B_{2}$)It is clear from eq1 and eq2 that $B_{1}>B_{2}$ ,therefore the direction of  $B$ will be along $PX$ .or    $B=$$\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{(r-l)^{2}}$$-\dfrac{\mu_{0}}{4\pi}.\dfrac{m}{(r+l)^{2}}$     (alongPX)or    $B=\dfrac{\mu_{0}}{4\pi}.\dfrac{m(4rl)}{(r^{2}-l^{2})^{2}}$     (alongPX)Now , $m(2l)=M$ (magnetic dipole moment of magnet)Hence , $B=\dfrac{\mu_{0}}{4\pi}.\dfrac{2Mr}{(r^{2}-l^{2})^{2}}$     (alongPX)

Question 4

$F_g$ and $F_e$ represent gravitational and electrostatic force respectively between electrons situated at a distance $0.1\,m. F_g/F_e$ is of the order

Accepted Answer

${ F }_{ y }$ and ${ F }_{ e }$ represent gravitational and electrostatic force respectively between electrons situated at a distance $=0.1m$let, us take the ratio$\dfrac { { F }_{ e } }{ { F }_{ g } } =\dfrac { \dfrac { 1 }{ 4\pi { \epsilon  }_{ 0 } } \dfrac { { q }^{ 2 } }{ { d }^{ 2 } }  }{ G\dfrac { { m }^{ 2 } }{ { d }^{ 2 } }  } $$\dfrac { { F }_{ e } }{ { F }_{ g } } =\dfrac { 1 }{ 4\pi { \epsilon  }_{ 0 } } \times \dfrac { 1 }{ G } \times \dfrac { { q }^{ 2 } }{ { m }^{ 2 } } $$\dfrac { { F }_{ e } }{ { F }_{ g } } =9\times { 10 }^{ 9 }\times \dfrac { 1 }{ 6.67\times { 10 }^{ -11 } } \times \dfrac { { \left( 1.6\times { 10 }^{ -19 } \right)  }^{ 2 } }{ { \left( 9.1\times { 10 }^{ -31 } \right)  }^{ 2 } } $$\Rightarrow \dfrac { { F }_{ e } }{ { F }_{ g } } =4.17\times { 10 }^{ 42 }$or,  $\dfrac { { F }_{ e } }{ { F }_{ g } } $ is of the order of ${ 10 }^{ -42 }$.

Question 5

The ratio of magnitude of electrostatic force and gravitational force for an electron and proton is

Accepted Answer

Here, for an electron and a protonElectrostatic force, $\left| { F }_{ e } \right| =\cfrac { 1 }{ 4\pi { \varepsilon  }_{ 0 } } \cfrac { { e }^{ 2 } }{ { r }^{ 2 } } $Gravitational force, $\left| { F }_{ g } \right| =\cfrac { G{ m }_{ e }{ m }_{ p } }{ { r }^{ 2 } } $$\therefore \cfrac { \left| { F }_{ e } \right|  }{ \left| { F }_{ g } \right|  } =\cfrac { 1 }{ 4\pi { \varepsilon  }_{ 0 } } \cfrac { { e }^{ 2 } }{ G{ m }_{ e }{ m } } =\cfrac { 9\times { 10 }^{ 9 }\times { \left( 1.6\times { 10 }^{ -19 } \right)  }^{ 2 } }{ 6.67\times { 10 }^{ -11 }\times 9\times { 10 }^{ -31 }\times 1.66\times { 10 }^{ -27 } } =2.4\times { 10 }^{ 39 }$

Question 6

Identify the poles of the magnet in the figure (a) and (b) shown below.

Accepted Answer

The magnetic field lines emerge from north pole and merge at the south pole

Question 7

What are magnetic field lines? How is the direction of magnetic field at a point in a magnetic field determined using field lines?

Accepted Answer

A magnetic field line is the path along which a free north-pole tends to move. The direction of a magnetic field at a point is determined by placing a small compass needle. The N - pole of compass indicates the direction of magnetic field at that point.

Question 8

The ratio of electric force to the gravitational force between two protons separated by a finite distance is of the order of:

Accepted Answer

$Gravitational\ force\ = \dfrac{G(m_p)^2}{r^2}$$Electric\ force\ = \dfrac{K(e)(e)}{r^2}$$Ratio\ = \dfrac{K(1.6\times 10^{-19})^2}{r^2}\times \dfrac{r^2}{G\times (1.6\ 7\times 10^{-27})^2}$$= \dfrac{(9\times 10^9)\times (1.6\times 10^{-19})^2}{(6.6\ 7\times 10^{-11})(1.6\ 7\times 10^{-27})^2}$$=1.23\times 10^{20}\times 10^{16}$$= 10^{36}$(order of magnitude)

Question 9

The given magnet is divided into three parts A, B and C.

A B C
Name the parts where the strength of the magnetic field is:
(i) maximum (ii) minimum
How will density of magnetic field lines differ at these parts.

Accepted Answer

(i) Maximum magnetic field is in the region A and C. (ii) Minimum magnetic field is in the region B. Reason: A and C are magnetic poles and have maximum number of magnetic field lines which determine the intensity of magnetic field while B is centre of the magnet has no magnetic field lines. So intensity of magnetic field near B is almost zero.

Question 10

Explain the magnetic elements of the earth's magnetic field.

Accepted Answer

The elements are:Magnetic declination (q)Magnetic inclination (d)Horizontal component (BH)&#8203;Magnetic declination:The small angle between magnetic axis and geographic axis at a place is defined as magnetic declination at that place. It is represented by &#952;.Magnetic Inclination:Magnetic dip, dip angle, or magnetic inclination is the angle made with the horizontal by the compass needle of a vertically held compass. This angle varies at different points on the Earth's surface. Positive values of inclination indicate that the magnetic field of the Earth is pointing downward, into the Earth, at the point of measurement. The value can be measured with an instrument typically known as a dip circle.(1)At equator the magnetic field is parallel to the horizon so there will be zero angle of dip.(2) At poles the magnetic field is almost vertical, here the dip will me maximum.Horizontal component :It is the component of earth&#8217;s magnetic field along the horizontal direction.So the angle of dip is the angle between earth&#8217;s magnetic field i.e. B and the horizontal component i.e. BH.

Revise with Concepts

Properties of Magnetic Field Lines Around a Bar Magnet

Quick Summary With Stories

Properties of Magnetic Field Lines Around a Bar Magnet

Why do magnetic field lines not intersect each other?

The magnetic field in a given region is uniform. Draw a diagram to represent it.

Derive an expression for magnetic field at a point on the axial line of a bar magnet.

$F_{g}$ and $F_{e}$ represent gravitational and electrostatic force respectively between electrons situated at a distance $0.1 m . F_{g} / F_{e}$ is of the order

The ratio of magnitude of electrostatic force and gravitational force for an electron and proton is

Identify the poles of the magnet in the figure (a) and (b) shown below.

What are magnetic field lines? How is the direction of magnetic field at a point in a magnetic field determined using field lines?

The ratio of electric force to the gravitational force between two protons separated by a finite distance is of the order of:

The given magnet is divided into three parts A, B and C.

A B C
Name the parts where the strength of the magnetic field is:
(i) maximum (ii) minimum
How will density of magnetic field lines differ at these parts.

Explain the magnetic elements of the earth's magnetic field.

Revise with Concepts

Properties of Magnetic Field Lines Around a Bar Magnet

Quick Summary With Stories

Properties of Magnetic Field Lines Around a Bar Magnet

Why do magnetic field lines not intersect each other?

The magnetic field in a given region is uniform. Draw a diagram to represent it.

Derive an expression for magnetic field at a point on the axial line of a bar magnet.

Fg​ and Fe​ represent gravitational and electrostatic force respectively between electrons situated at a distance 0.1m.Fg​/Fe​ is of the order

The ratio of magnitude of electrostatic force and gravitational force for an electron and proton is

Identify the poles of the magnet in the figure (a) and (b) shown below.

What are magnetic field lines? How is the direction of magnetic field at a point in a magnetic field determined using field lines?

The ratio of electric force to the gravitational force between two protons separated by a finite distance is of the order of:

The given magnet is divided into three parts A, B and C. ABCName the parts where the strength of the magnetic field is: (i) maximum (ii) minimum How will density of magnetic field lines differ at these parts.

Explain the magnetic elements of the earth's magnetic field.

$F_{g}$ and $F_{e}$ represent gravitational and electrostatic force respectively between electrons situated at a distance $0.1 m . F_{g} / F_{e}$ is of the order

The given magnet is divided into three parts A, B and C.

A B C
Name the parts where the strength of the magnetic field is:
(i) maximum (ii) minimum
How will density of magnetic field lines differ at these parts.