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Question: Two identical magnetic dipoles of magnetic moments 1.0 A-m<sup>2</sup> each, placed at a separation ...

Two identical magnetic dipoles of magnetic moments 1.0 A-m2 each, placed at a separation of 2m with their axis perpendicular to each other. The resultant magnetic field at a point midway between the dipoles is

A

5×10−7T5 \times 10 ^ { - 7 } T

B

5×10−7T\sqrt { 5 } \times 10 ^ { - 7 } T

C

T2\frac { T } { 2 }

D

None

Answer

5×10−7T\sqrt { 5 } \times 10 ^ { - 7 } T

Explanation

Solution

B1=μ04π⋅2M(r2)3=10−7×2×1(22)3\mathrm { B } _ { 1 } = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 2 \mathrm { M } } { \left( \frac { \mathrm { r } } { 2 } \right) ^ { 3 } } = 10 ^ { - 7 } \times \frac { 2 \times 1 } { \left( \frac { 2 } { 2 } \right) ^ { 3 } };

;

Bnet =(2×10−7)2+(10−7)2=5×10−7 TB _ { \text {net } } = \sqrt { \left( 2 \times 10 ^ { - 7 } \right) ^ { 2 } + \left( 10 ^ { - 7 } \right) ^ { 2 } } = \sqrt { 5 } \times 10 ^ { - 7 } \mathrm {~T}