<P> Where V (\ displaystyle V) is the volume of the magnet . For a cylinder this is V = π R 2 L (\ displaystyle V = \ pi R ^ (2) L). </P> <P> When L ≪ x (\ displaystyle L \ ll x) the point dipole approximation is obtained, </P> <Dl> <Dd> F (x) = 3 π μ 0 2 M 2 R 4 L 2 1 x 4 = 3 μ 0 2 π M 2 V 2 1 x 4 = 3 μ 0 2 π m 1 m 2 1 x 4 (\ displaystyle F (x) = (\ frac (3 \ pi \ mu _ (0)) (2)) M ^ (2) R ^ (4) L ^ (2) (\ frac (1) (x ^ (4))) = (\ frac (3 \ mu _ (0)) (2 \ pi)) M ^ (2) V ^ (2) (\ frac (1) (x ^ (4))) = (\ frac (3 \ mu _ (0)) (2 \ pi)) m_ (1) m_ (2) (\ frac (1) (x ^ (4)))) </Dd> </Dl> <Dd> F (x) = 3 π μ 0 2 M 2 R 4 L 2 1 x 4 = 3 μ 0 2 π M 2 V 2 1 x 4 = 3 μ 0 2 π m 1 m 2 1 x 4 (\ displaystyle F (x) = (\ frac (3 \ pi \ mu _ (0)) (2)) M ^ (2) R ^ (4) L ^ (2) (\ frac (1) (x ^ (4))) = (\ frac (3 \ mu _ (0)) (2 \ pi)) M ^ (2) V ^ (2) (\ frac (1) (x ^ (4))) = (\ frac (3 \ mu _ (0)) (2 \ pi)) m_ (1) m_ (2) (\ frac (1) (x ^ (4)))) </Dd>

Does a magnet have to be touching another material to exert a force