(a) Define mutual inductance and write its S.I. unit.
(b) A square loop of side ‘a’ carrying a current I₂ is kept at distance x from an infinitely long straight wire carrying a current I₁ as shown in the figure. Obtain the expression for the resultant force acting on the loop.

Question

(a) Define mutual inductance and write its S.I. unit.
(b) A square loop of side ‘a’ carrying a current I₂ is kept at distance x from an infinitely long straight wire carrying a current I₁ as shown in the figure. Obtain the expression for the resultant force acting on the loop.

Philoid · Accepted Answer

(a) Mutual inductance is the property of two coils that opposes the change in current in one coil.

There are two Coils: coil 1 and coil2 with the number of turns N₁ and N₂. The magnetic flux across them is and respectively. Let the current through coil 1 be and current through coil 2 be . Then, the mutual-inductance is given by:

(b)

Concepts/Formulas used:

Force between two wires:

If two straight infinite parallel conducting wires with current and are separated by a distance , then force per unit length of each wire is given by:

where is the magnetic permeability of free space.

If the wires carry currents in the same direction, they attract and if they carry currents in opposite direction, they repel.

By symmetry, and must be equal. Hence, they cancel out.

Now,

Also,

The total force is

(a) Define mutual inductance and write its S.I. unit.(b) A square loop of side ‘a’ carrying a current I2 is kept at distance x from an infinitely long straight wire carrying a current I1 as shown in the figure. Obtain the expression for the resultant force acting on the loop.

(a) Define mutual inductance and write its S.I. unit.
(b) A square loop of side ‘a’ carrying a current I₂ is kept at distance x from an infinitely long straight wire carrying a current I₁ as shown in the figure. Obtain the expression for the resultant force acting on the loop.