360640
Two identical magnetic dipoles are placed as shown in figure separated by distance \(d\). The magnetic field midway between the dipole is
1 \(\dfrac{\mu_{0} M \sqrt{5}}{4 \pi d^{3}}\)
2 \(\dfrac{2 \mu_{0} M \sqrt{5}}{\pi d^{3}}\)
3 \(\dfrac{\mu_{0} M \sqrt{2}}{4 \pi d^{3}}\)
4 None of these
Explanation:
Resultant field \(B=\sqrt{B_{1}^{2}+B_{2}^{2}}\) \(=\dfrac{\mu_{0} M}{4 \pi\left(\dfrac{d}{2}\right)^{3}} \sqrt{1^{2}+2^{2}}=\dfrac{2 \mu_{0} M \sqrt{5}}{\pi d^{3}}\)
PHXII05:MAGNETISM and MATTER
360641
Two short bar magnets of equal dipole moment \(M\) are fastened perpendicularly at their centres as shown in figure. The magnitude of resultant of two magnetic field at a distance \(d\) from the centre on the bisector line of the right angle is
Resolving the magnetic moments along \(OP\) and perpendicular to \(OP\), we find that component of fields perpendicular to \(OP\) cancel out. Resultant magnetic moment along \(OP\) \(\begin{aligned}& =M \cos 45^{\circ}+M \cos 45^{\circ} \\& =2 M \cos 45^{\circ}=\dfrac{2 M}{\sqrt{2}}=\sqrt{2} M\end{aligned}\) The point \(P\) lies on axial line of magnet of moment \( = \sqrt 2 M\) \(\therefore B = \frac{{{\mu _0}}}{{4\pi }}\frac{{2\sqrt 2 M}}{{{d^3}}}\)
PHXII05:MAGNETISM and MATTER
360642
The magnetic field due to dipole of magnetic moment \(1.2A{m^2}\) at a point 1\(m\) away from it and making an angle \(60^{\circ}\) with axis of the dipole is
360640
Two identical magnetic dipoles are placed as shown in figure separated by distance \(d\). The magnetic field midway between the dipole is
1 \(\dfrac{\mu_{0} M \sqrt{5}}{4 \pi d^{3}}\)
2 \(\dfrac{2 \mu_{0} M \sqrt{5}}{\pi d^{3}}\)
3 \(\dfrac{\mu_{0} M \sqrt{2}}{4 \pi d^{3}}\)
4 None of these
Explanation:
Resultant field \(B=\sqrt{B_{1}^{2}+B_{2}^{2}}\) \(=\dfrac{\mu_{0} M}{4 \pi\left(\dfrac{d}{2}\right)^{3}} \sqrt{1^{2}+2^{2}}=\dfrac{2 \mu_{0} M \sqrt{5}}{\pi d^{3}}\)
PHXII05:MAGNETISM and MATTER
360641
Two short bar magnets of equal dipole moment \(M\) are fastened perpendicularly at their centres as shown in figure. The magnitude of resultant of two magnetic field at a distance \(d\) from the centre on the bisector line of the right angle is
Resolving the magnetic moments along \(OP\) and perpendicular to \(OP\), we find that component of fields perpendicular to \(OP\) cancel out. Resultant magnetic moment along \(OP\) \(\begin{aligned}& =M \cos 45^{\circ}+M \cos 45^{\circ} \\& =2 M \cos 45^{\circ}=\dfrac{2 M}{\sqrt{2}}=\sqrt{2} M\end{aligned}\) The point \(P\) lies on axial line of magnet of moment \( = \sqrt 2 M\) \(\therefore B = \frac{{{\mu _0}}}{{4\pi }}\frac{{2\sqrt 2 M}}{{{d^3}}}\)
PHXII05:MAGNETISM and MATTER
360642
The magnetic field due to dipole of magnetic moment \(1.2A{m^2}\) at a point 1\(m\) away from it and making an angle \(60^{\circ}\) with axis of the dipole is
360640
Two identical magnetic dipoles are placed as shown in figure separated by distance \(d\). The magnetic field midway between the dipole is
1 \(\dfrac{\mu_{0} M \sqrt{5}}{4 \pi d^{3}}\)
2 \(\dfrac{2 \mu_{0} M \sqrt{5}}{\pi d^{3}}\)
3 \(\dfrac{\mu_{0} M \sqrt{2}}{4 \pi d^{3}}\)
4 None of these
Explanation:
Resultant field \(B=\sqrt{B_{1}^{2}+B_{2}^{2}}\) \(=\dfrac{\mu_{0} M}{4 \pi\left(\dfrac{d}{2}\right)^{3}} \sqrt{1^{2}+2^{2}}=\dfrac{2 \mu_{0} M \sqrt{5}}{\pi d^{3}}\)
PHXII05:MAGNETISM and MATTER
360641
Two short bar magnets of equal dipole moment \(M\) are fastened perpendicularly at their centres as shown in figure. The magnitude of resultant of two magnetic field at a distance \(d\) from the centre on the bisector line of the right angle is
Resolving the magnetic moments along \(OP\) and perpendicular to \(OP\), we find that component of fields perpendicular to \(OP\) cancel out. Resultant magnetic moment along \(OP\) \(\begin{aligned}& =M \cos 45^{\circ}+M \cos 45^{\circ} \\& =2 M \cos 45^{\circ}=\dfrac{2 M}{\sqrt{2}}=\sqrt{2} M\end{aligned}\) The point \(P\) lies on axial line of magnet of moment \( = \sqrt 2 M\) \(\therefore B = \frac{{{\mu _0}}}{{4\pi }}\frac{{2\sqrt 2 M}}{{{d^3}}}\)
PHXII05:MAGNETISM and MATTER
360642
The magnetic field due to dipole of magnetic moment \(1.2A{m^2}\) at a point 1\(m\) away from it and making an angle \(60^{\circ}\) with axis of the dipole is
360640
Two identical magnetic dipoles are placed as shown in figure separated by distance \(d\). The magnetic field midway between the dipole is
1 \(\dfrac{\mu_{0} M \sqrt{5}}{4 \pi d^{3}}\)
2 \(\dfrac{2 \mu_{0} M \sqrt{5}}{\pi d^{3}}\)
3 \(\dfrac{\mu_{0} M \sqrt{2}}{4 \pi d^{3}}\)
4 None of these
Explanation:
Resultant field \(B=\sqrt{B_{1}^{2}+B_{2}^{2}}\) \(=\dfrac{\mu_{0} M}{4 \pi\left(\dfrac{d}{2}\right)^{3}} \sqrt{1^{2}+2^{2}}=\dfrac{2 \mu_{0} M \sqrt{5}}{\pi d^{3}}\)
PHXII05:MAGNETISM and MATTER
360641
Two short bar magnets of equal dipole moment \(M\) are fastened perpendicularly at their centres as shown in figure. The magnitude of resultant of two magnetic field at a distance \(d\) from the centre on the bisector line of the right angle is
Resolving the magnetic moments along \(OP\) and perpendicular to \(OP\), we find that component of fields perpendicular to \(OP\) cancel out. Resultant magnetic moment along \(OP\) \(\begin{aligned}& =M \cos 45^{\circ}+M \cos 45^{\circ} \\& =2 M \cos 45^{\circ}=\dfrac{2 M}{\sqrt{2}}=\sqrt{2} M\end{aligned}\) The point \(P\) lies on axial line of magnet of moment \( = \sqrt 2 M\) \(\therefore B = \frac{{{\mu _0}}}{{4\pi }}\frac{{2\sqrt 2 M}}{{{d^3}}}\)
PHXII05:MAGNETISM and MATTER
360642
The magnetic field due to dipole of magnetic moment \(1.2A{m^2}\) at a point 1\(m\) away from it and making an angle \(60^{\circ}\) with axis of the dipole is
