In the given figure, two points P and Q are located at distances r and r respectively from a - Physics - Magnetism And Matter

Question

In the given figure, two points P and Q are located at
distances r and
r’ respectively from a bar
magnet

Assume that the distance r
is much greater than the length of the magnet If
r = 2 r’
, then what is the ratio of magnitude of magnetic fields at P
and Q?

Vijay Yadav · Accepted Answer

Assume pole strength = m Length of bar magnet = 2l The magnetic field at P due to north pole is $B_{N} = \frac{µ_{0}}{4 π} \frac{m}{{(r + 2 l)}^{2}}$ directed away from magnet The field due to south pole $B_{S} = \frac{µ_{0}}{4 π} \frac{m}{r^{2}}$ directed towards the magnet the resultant field BP = BS â€“ BN $= \frac{µ_{0} m}{4 π} [\frac{1}{r^{2}} - \frac{1}{(r + 2 l)^{2}}]$ (1) $\vec{B_{S}} = \frac{µ_{0}}{4 π} \frac{m \vec{QS}}{(SQ)^{3}} \vec{B_{N}} = \frac{µ_{0}}{4 π} \frac{m \vec{NQ}}{(NQ)^{3}}$

NQ = SQ = (r1 + l)1/2 $SO \vec{B_{Q}} = \vec{B_{N}} + \vec{B_{S}} = \frac{µ_{0}}{4 π} \frac{m}{(r^{1} + l^{2})^{\frac{3}{2}}} (\vec{NQ} + \vec{QS}) = \frac{µ_{0}}{4 π} \frac{m (\vec{NS})}{(r^{1} + l^{2})^{\frac{3}{2}}} B_{Q} = | \vec{B_{Q}} | = \frac{µ_{0}}{4 π} \frac{m (2 l)}{{(r^{1} + l^{2})}^{\frac{3}{2}}}$ (2) Divide eqn(1) and (2) and apply the approximation

In the given figure, two points P and Q are located at distances r and r’ respectively from a bar magnet. Assume that the distance r is much greater than the length of the magnet. If r = 2 r’ , then what is the ratio of magnitude of magnetic fields at P and Q?.

In the given figure, two points P and Q are located at distances r and r’ respectively from a bar magnet.

Assume that the distance r is much greater than the length of the magnet. If r = 2 r’ , then what is the ratio of magnitude of magnetic fields at P and Q?.