Question

Two short magnetic dipoles are arranged coaxially, as shown in the diagram. At which point on their common axis, the resultant magnetic field, might be zero?

• A. in a region between the two dipoles, on the common axis, closer to $M_2$
• B. in a region to the left of both the dipoles
• C. in a region between the two dipoles, on the common axis, closer to $M_1$
• D. Such point will not exist anywhere on the common axis of $M_1$ and $M_2$

Answer 1

The correct option is C in a region between the two dipoles, on the common axis, closer to $M_1$


Consider three points $\text{P},\text{Q}$ and $\text{R}$ as shown in the diagram. Let $\overrightarrow{B_1}$ and $\overrightarrow{B_2}$ be the magnetic fields due to the dipoles $M_1$ and $M_2$ respectively.

At point $\text{P}$, the resultant magnetic field cannot be zero as $|\overrightarrow{B_2}|>|\overrightarrow{B_1}|$

At point $\text{Q}$, the resultant magnetic field can be zero as $|\overrightarrow{B_2}|$ may be equal to $|\overrightarrow{B_1}|$, at one point (closer to $M_1$)

At point R, the resultant magnetic field can be zero as $|\overrightarrow{B_2}|$ may be equal to $|\overrightarrow{B_1}|$, at one point.

Hence, option ($C$) is the correct answer.