Ncert Exercises & Solutions

Do magnetic forces obey Newton’s third law. Verify for two current elements ${dl}_{1}$ = dl $\hat{i}$ located at the origin and ${dl}_{2} = dl \hat{j}$ located at (0, R, 0). Both carry current I.

Hint: Find the action-reaction forces.

Step 1: In Biot-Savart's law, the magnetic field B is parallel to (idl x r) and idl have its direction along the direction of flow of current.

Here, for the direction of the magnetic field at

{dl}_{2}

, located at (0, R, 0) due to wire

{dl}_{1}

is given by B || (idl x r) or

\hat{i} \times \hat{j}

(because point (0, R, 0) lies on the y-axis). but

\hat{i} \times \hat{j} = \hat{k}

So, the direction of the magnetic field at

{dl}_{2}

is along the z-direction.

The direction of the magnetic force exerted at

{dl}_{2}

due to the first wire along the x-axis;

F = i(l x B) i.e., F ||

\hat{i} \times \hat{k}

or along -

\hat{j}

direction.

Therefore, the force due to

{dl}_{1}

{dl}_{2}

is non-zero.

Step 2: Now, for the direction of the magnetic field at

{dl}_{1}

located at (0, 0, 0) due to wire

{dl}_{2}

is given by;

B || (idl x r) or

\hat{j} \times - \hat{j}

(because origin lies on y-direction w.r.t. point (0, R, 0).), but

\hat{j} \times - \hat{j}

= 0.

So, the magnetic field at

{dl}_{1}

does not exist.

Force due to

{dl}_{2} on {dl}_{1}

is zero.

So, the magnetic forces do not obey Newton's third law.

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