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  • Do magnetic forces obey Newton’s third law. Verify for two current elements dl_1 = dl i located at the origin and dl_2 = dl j located at(0, R, 0). Both carry current I.

Do magnetic forces obey Newton’s third law. Verify for two current elements dl_1 = dl i located at the origin and dl_2 = dl j located at(0, R, 0). Both carry current I.

Answers (1)

To solve the problem, we need to determine the magnetic field’s direction caused by one wire at the point on other wire, then calculate the magnetic force on the current-carrying wire.

As according to Biot-Savart’s law, idl is the current-carrying element along the direction of the flow, and magnetic field B is parallel to idl \times r.

The direction of the magnetic field is given by B || idl \times r or i \times j (because point (0, R, 0) lies ony-axis), but i \times j = k which is present at idl _{2} and located at located at (0, R, 0) due to the wire dlx.

This makes the direction the magnetic field along z-direction at dl _{2}.

And the magnetic field present at dl2 due to the magnetic field of first wire has its direction in the x-axis.

F-i(l \times B), i.e., F||(i \times k) or along – j direction.

Therefore, it makes the forces present due to dl[ on dl _{2} is non-zero.

Now, to find he direction of the magnetic field at dx due to the d_{2} wire located at (0, 0, 0) is calculated by the relationB||idl \times r or j \times -j(because origin lies on y-direction with respect to the point (0, R, 0), but j \times - j = 0.

 This implies that there is no magnetic field present at dx.

Hence, force due to dl _{2} on dl_{1}, is zero.

So,Newton’s third law is not followed by the magnetic forces. But in case of current carrying elements present parallel to each other they will follow Newton’s third law.

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