As discussed earlier, the force exerted by a dipole loop with moment m 1 on another with moment m 2 is F = ∇ ∇ ( m 2 ⋅ ⋅ B 1 ) , where B 1 is the magnetic field due to moment m 1. The result of calculating the gradient is F ( r , m 1 , m 2 ) = 3 μ μ 0 4 π π | r | 4 [ m 2 ( m 1 ⋅ ⋅ r ^ ^ ) + m 1 ( m 2 ⋅ ⋅ r ^ ^ ) + r ^ ^ ( m 1 ⋅ ⋅ m 2 ) − − 5 r ^ ^ ( m 1 ⋅ ⋅ r ^ ^ ) ( m 2 ⋅ ⋅ r ^ ^ ) ] , where r̂ is the unit vector pointing from magnet 1 to magnet 2 and r is the distance. An equivalent expression is F = 3 μ μ 0 4 π π | r | 4 [ ( r ^ ^ × × m 1 ) × × m 2 + ( r ^ ^ × × m 2 ) × × m 1 − − 2 r ^ ^ ( m 1 ⋅ ⋅ m 2 ) + 5 r ^ ^ ( r ^ ^ × × m 1 ) ⋅ ⋅ ( r ^ ^ × × m 2 ) ] . The force acting on m 1 is in the opposite direction.