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PHXII04:MOVING CHARGES AND MAGNETISM

362677 For a circular current carrying loop having a magnetic moment $\vec{m}$ , the magnetic field $\vec{B}$ , at a distance $x$ on the axis of the loop $(x >> R)$ is

1

\frac{- μ_{0}}{4 π} \frac{\vec{m}}{x^{3}}

2

\frac{μ_{0}}{4 π} \frac{\vec{m}}{x^{3}}

3

\frac{- μ_{0}}{4 π} \frac{2 \vec{m}}{x^{3}}

4

\frac{μ_{0}}{4 π} \frac{2 \vec{m}}{x^{3}}

Explanation:

For an electric dipole, the electric field on the axis of the dipole is $\vec{E} = \frac{2 K \vec{P}}{x^{3}}$
Here by analogy, we replace $\vec{E}$ by $\vec{B}, K$ by $\frac{μ_{0}}{4 π}$ and $\vec{P}$ by $\vec{m}$ .

PHXII04:MOVING CHARGES AND MAGNETISM

362678 The magnetic field at the centre of a circular current carrying conductor of radius $r$ is $B_{c}$ . The magnetic field on its axis at a distance $r$ from the centre is $B_{a}$ . The value of $B_{c} : B_{a}$ will be

1

2 \sqrt{2} : 1

2

\sqrt{2} : 1

3

1 : \sqrt{2}

4

1 : 2 \sqrt{2}

Explanation:

The magnetic induction at the centre of circular wire $= \frac{μ_{0}}{4 π} \frac{2 π i}{r}$
Along the axis at a distance $r$ from the centre,
$= \frac{μ_{0}}{4 π r} \frac{2 π i}{2 \sqrt{2}}$
$∴ \frac{B_{c}}{B_{r - a x i a l}} = 2 \sqrt{2} : 1$

KCET - 2008

PHXII04:MOVING CHARGES AND MAGNETISM

362679 Assertion :
In circular loop of wire. perpendicular components of magnetic field at some distance trom centre of loop turned over the whole loop cancel.
Reason :
The resultant of magnetic field on axial point of circular loop is due to axial component of field.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

supporting img
In a circular loop, the perpendicular components of magnetic fields from diametrically opposite elements cancel out along the loop's axis, leaving only the $x$ -components contributing to the net magnetic field along the $x$ -axis. So correct option is (1).

PHXII04:MOVING CHARGES AND MAGNETISM

362680 Assertion :
For a point on the axis of a circular coil carrying current, magnetic field is maximum at the centre of the coil.
Reason :
Magnetic field is inversely proportional to the distance of point from the circular coil.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$B = \frac{μ_{0} N I}{2 r}$
the magnetic field at the center of a circular coil is maximum. The reason accurately explains that the magnetic field is inversely proportional to the distance from the coil, with the basis for the maximum field at the center.
$(r \to 0$ ,
$B \to B_{max})$
So correct option is (1).

PHXII04:MOVING CHARGES AND MAGNETISM

362677 For a circular current carrying loop having a magnetic moment $\vec{m}$ , the magnetic field $\vec{B}$ , at a distance $x$ on the axis of the loop $(x >> R)$ is

1

\frac{- μ_{0}}{4 π} \frac{\vec{m}}{x^{3}}

2

\frac{μ_{0}}{4 π} \frac{\vec{m}}{x^{3}}

3

\frac{- μ_{0}}{4 π} \frac{2 \vec{m}}{x^{3}}

4

\frac{μ_{0}}{4 π} \frac{2 \vec{m}}{x^{3}}

Explanation:

For an electric dipole, the electric field on the axis of the dipole is $\vec{E} = \frac{2 K \vec{P}}{x^{3}}$
Here by analogy, we replace $\vec{E}$ by $\vec{B}, K$ by $\frac{μ_{0}}{4 π}$ and $\vec{P}$ by $\vec{m}$ .

PHXII04:MOVING CHARGES AND MAGNETISM

362678 The magnetic field at the centre of a circular current carrying conductor of radius $r$ is $B_{c}$ . The magnetic field on its axis at a distance $r$ from the centre is $B_{a}$ . The value of $B_{c} : B_{a}$ will be

1

2 \sqrt{2} : 1

2

\sqrt{2} : 1

3

1 : \sqrt{2}

4

1 : 2 \sqrt{2}

Explanation:

The magnetic induction at the centre of circular wire $= \frac{μ_{0}}{4 π} \frac{2 π i}{r}$
Along the axis at a distance $r$ from the centre,
$= \frac{μ_{0}}{4 π r} \frac{2 π i}{2 \sqrt{2}}$
$∴ \frac{B_{c}}{B_{r - a x i a l}} = 2 \sqrt{2} : 1$

KCET - 2008

PHXII04:MOVING CHARGES AND MAGNETISM

362679 Assertion :
In circular loop of wire. perpendicular components of magnetic field at some distance trom centre of loop turned over the whole loop cancel.
Reason :
The resultant of magnetic field on axial point of circular loop is due to axial component of field.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

supporting img
In a circular loop, the perpendicular components of magnetic fields from diametrically opposite elements cancel out along the loop's axis, leaving only the $x$ -components contributing to the net magnetic field along the $x$ -axis. So correct option is (1).

PHXII04:MOVING CHARGES AND MAGNETISM

362680 Assertion :
For a point on the axis of a circular coil carrying current, magnetic field is maximum at the centre of the coil.
Reason :
Magnetic field is inversely proportional to the distance of point from the circular coil.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$B = \frac{μ_{0} N I}{2 r}$
the magnetic field at the center of a circular coil is maximum. The reason accurately explains that the magnetic field is inversely proportional to the distance from the coil, with the basis for the maximum field at the center.
$(r \to 0$ ,
$B \to B_{max})$
So correct option is (1).

PHXII04:MOVING CHARGES AND MAGNETISM

362677 For a circular current carrying loop having a magnetic moment $\vec{m}$ , the magnetic field $\vec{B}$ , at a distance $x$ on the axis of the loop $(x >> R)$ is

1

\frac{- μ_{0}}{4 π} \frac{\vec{m}}{x^{3}}

2

\frac{μ_{0}}{4 π} \frac{\vec{m}}{x^{3}}

3

\frac{- μ_{0}}{4 π} \frac{2 \vec{m}}{x^{3}}

4

\frac{μ_{0}}{4 π} \frac{2 \vec{m}}{x^{3}}

Explanation:

For an electric dipole, the electric field on the axis of the dipole is $\vec{E} = \frac{2 K \vec{P}}{x^{3}}$
Here by analogy, we replace $\vec{E}$ by $\vec{B}, K$ by $\frac{μ_{0}}{4 π}$ and $\vec{P}$ by $\vec{m}$ .

PHXII04:MOVING CHARGES AND MAGNETISM

362678 The magnetic field at the centre of a circular current carrying conductor of radius $r$ is $B_{c}$ . The magnetic field on its axis at a distance $r$ from the centre is $B_{a}$ . The value of $B_{c} : B_{a}$ will be

1

2 \sqrt{2} : 1

2

\sqrt{2} : 1

3

1 : \sqrt{2}

4

1 : 2 \sqrt{2}

Explanation:

The magnetic induction at the centre of circular wire $= \frac{μ_{0}}{4 π} \frac{2 π i}{r}$
Along the axis at a distance $r$ from the centre,
$= \frac{μ_{0}}{4 π r} \frac{2 π i}{2 \sqrt{2}}$
$∴ \frac{B_{c}}{B_{r - a x i a l}} = 2 \sqrt{2} : 1$

KCET - 2008

PHXII04:MOVING CHARGES AND MAGNETISM

362679 Assertion :
In circular loop of wire. perpendicular components of magnetic field at some distance trom centre of loop turned over the whole loop cancel.
Reason :
The resultant of magnetic field on axial point of circular loop is due to axial component of field.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

supporting img
In a circular loop, the perpendicular components of magnetic fields from diametrically opposite elements cancel out along the loop's axis, leaving only the $x$ -components contributing to the net magnetic field along the $x$ -axis. So correct option is (1).

PHXII04:MOVING CHARGES AND MAGNETISM

362680 Assertion :
For a point on the axis of a circular coil carrying current, magnetic field is maximum at the centre of the coil.
Reason :
Magnetic field is inversely proportional to the distance of point from the circular coil.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$B = \frac{μ_{0} N I}{2 r}$
the magnetic field at the center of a circular coil is maximum. The reason accurately explains that the magnetic field is inversely proportional to the distance from the coil, with the basis for the maximum field at the center.
$(r \to 0$ ,
$B \to B_{max})$
So correct option is (1).

PHXII04:MOVING CHARGES AND MAGNETISM

362677 For a circular current carrying loop having a magnetic moment $\vec{m}$ , the magnetic field $\vec{B}$ , at a distance $x$ on the axis of the loop $(x >> R)$ is

1

\frac{- μ_{0}}{4 π} \frac{\vec{m}}{x^{3}}

2

\frac{μ_{0}}{4 π} \frac{\vec{m}}{x^{3}}

3

\frac{- μ_{0}}{4 π} \frac{2 \vec{m}}{x^{3}}

4

\frac{μ_{0}}{4 π} \frac{2 \vec{m}}{x^{3}}

Explanation:

For an electric dipole, the electric field on the axis of the dipole is $\vec{E} = \frac{2 K \vec{P}}{x^{3}}$
Here by analogy, we replace $\vec{E}$ by $\vec{B}, K$ by $\frac{μ_{0}}{4 π}$ and $\vec{P}$ by $\vec{m}$ .

PHXII04:MOVING CHARGES AND MAGNETISM

362678 The magnetic field at the centre of a circular current carrying conductor of radius $r$ is $B_{c}$ . The magnetic field on its axis at a distance $r$ from the centre is $B_{a}$ . The value of $B_{c} : B_{a}$ will be

1

2 \sqrt{2} : 1

2

\sqrt{2} : 1

3

1 : \sqrt{2}

4

1 : 2 \sqrt{2}

Explanation:

The magnetic induction at the centre of circular wire $= \frac{μ_{0}}{4 π} \frac{2 π i}{r}$
Along the axis at a distance $r$ from the centre,
$= \frac{μ_{0}}{4 π r} \frac{2 π i}{2 \sqrt{2}}$
$∴ \frac{B_{c}}{B_{r - a x i a l}} = 2 \sqrt{2} : 1$

KCET - 2008

PHXII04:MOVING CHARGES AND MAGNETISM

362679 Assertion :
In circular loop of wire. perpendicular components of magnetic field at some distance trom centre of loop turned over the whole loop cancel.
Reason :
The resultant of magnetic field on axial point of circular loop is due to axial component of field.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

supporting img
In a circular loop, the perpendicular components of magnetic fields from diametrically opposite elements cancel out along the loop's axis, leaving only the $x$ -components contributing to the net magnetic field along the $x$ -axis. So correct option is (1).

PHXII04:MOVING CHARGES AND MAGNETISM

362680 Assertion :
For a point on the axis of a circular coil carrying current, magnetic field is maximum at the centre of the coil.
Reason :
Magnetic field is inversely proportional to the distance of point from the circular coil.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$B = \frac{μ_{0} N I}{2 r}$
the magnetic field at the center of a circular coil is maximum. The reason accurately explains that the magnetic field is inversely proportional to the distance from the coil, with the basis for the maximum field at the center.
$(r \to 0$ ,
$B \to B_{max})$
So correct option is (1).

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