Two magnetic isolated north poles each of strength m A m, are placed one at each of the two vertices of an equilateral triangle of side α . The resultant magnetic induction at the third vertex is: ( μ 0 is permeability of free space)

Question

Two magnetic isolated north poles each of strength m A m, are placed one at each of the two vertices of an equilateral triangle of side α . The resultant magnetic induction at the third vertex is: ( μ 0 is permeability of free space) (A)  (μ 0/4π )( (m/a2) )  (B)  (μ 0/4π )(√2m/a2)  (C)  (μ 0/4π )(√3 m/a2)  (D)  (μ 0m/2π a2)

Tardigrade Admin · Accepted Answer

Magnetic field at the equatorial line when isolated north pole place at B.

B_{1} = \frac{μ _{0}}{4 π} \times \frac{m}{a ^{2}}

Similarly,

B_{2} = \frac{μ _{0}}{4 π} \times \frac{m}{a ^{2}}

Now, resultant magnetic field is

B_{res u l t a n t} = B_{1}^{2} + B_{2}^{2} + 2 B_{1} B_{2} cos 60^{o}

= B^{2} + B^{2} + 2 B^{2} \times \frac{1}{2}

= 3 B^{2} = 3 B = 3 \frac{μ _{0}}{4 π} \times \frac{m}{a ^{2}}

Q. Two magnetic isolated north poles each of strength m A m, are placed one at each of the two vertices of an equilateral triangle of side $α$ . The resultant magnetic induction at the third vertex is: ( $μ_{0}$ is permeability of free space)

$\frac{μ _{0}}{4 π} (\frac{m}{a ^{2}})$

$\frac{μ _{0}}{4 π} \frac{2 m}{a ^{2}}$

$\frac{μ _{0}}{4 π} \frac{3 m}{a ^{2}}$

$\frac{μ _{0} m}{2 π a ^{2}}$

Q. Two magnetic isolated north poles each of strength m A m, are placed one at each of the two vertices of an equilateral triangle of side α . The resultant magnetic induction at the third vertex is: ( μ0​ is permeability of free space)

4πμ0​​(a2m​)

4πμ0​​a22​m​

4πμ0​​a23​m​

2πa2μ0​m​

Magnetic field at the equatorial line when isolated north pole place at B. B1​=4πμ0​​×a2m​ Similarly, B2​=4πμ0​​×a2m​ Now, resultant magnetic field is Bresultant​=B12​+B22​+2B1​B2​cos60o​ =B2+B2+2B2×21​​ =3B2​=3B​=3​4πμ0​​×a2m​

Q. Two magnetic isolated north poles each of strength m A m, are placed one at each of the two vertices of an equilateral triangle of side $α$ . The resultant magnetic induction at the third vertex is: ( $μ_{0}$ is permeability of free space)

$\frac{μ _{0}}{4 π} (\frac{m}{a ^{2}})$

$\frac{μ _{0}}{4 π} \frac{2 m}{a ^{2}}$

$\frac{μ _{0}}{4 π} \frac{3 m}{a ^{2}}$

$\frac{μ _{0} m}{2 π a ^{2}}$