Magnetics 3 Question 3
3. Two coaxial solenoids of different radii carry current $I$ in the same direction. Let $\mathbf{F} _1$ be the magnetic force on the inner solenoid due to the outer one and $\mathbf{F} _2$ be the magnetic force on the outer solenoid due to the inner one. Then, (2015 Main)
(a) $\mathbf{F} _1$ is radially outwards and $\mathbf{F} _2=0$
(b) $\mathbf{F} _1$ is radially inwards and $\mathbf{F} _2$ is radially outwards
(c) $\mathbf{F} _1$ is radially inwards and $\mathbf{F} _2=0$
(d) $\mathbf{F} _1=\mathbf{F} _2=0$
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Answer:
Correct Answer: 3. (d)
Solution:
$$ \begin{aligned} & P \otimes \otimes \otimes \quad \otimes \quad \otimes \\ & Q \otimes \quad \otimes \quad \otimes \quad \otimes \quad \otimes \quad \otimes \end{aligned} $$
$$ S \odot \odot \odot \quad \odot \quad \odot \quad \odot $$
If we calculate the force on inner solenoid. Force on $Q$ due to $P$ is outwards (attraction between currents in same direction. Similarly, force on $R$ due to $S$ is also outwards. Hence, net force $\mathbf{F} _1$ is zero)
Force on $P$ due to $Q$ and force on $S$ due to $R$ is inwards. Hence, net force $\mathbf{F} _2$ is also zero.
Alternate Thought Field of one solenoid is uniform and other solenoid may be assumed a combination of circular closed loops. In uniform magnetic field, net force on a closed current carrying loop is zero.
