MHT CET · Physics · Magnetic Effects of Current

Figure show the circular coil carrying current $l$ kept very close but not touching at a point A on a straight conductor carrying the same current $l$ . The magnitude of magnetic induction at the centre of the circular coil will be

A $\frac{μ_{0} i}{2 r} [1 - \frac{1}{π}]$
B $\frac{μ_{0} l}{2 π r}$
C $\frac{μ_{0} l}{2 r}$
D Zero

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{μ_{0} i}{2 r} [1 - \frac{1}{π}]$

Step-by-step Solution

Detailed explanation

Magnetic induction at the centre of circular current carrying loop,

B_{1} = \frac{μ_{0} i}{2 r}

(downward direction)
Magnetic induction at the centre O due to a straight wire,

B_{2} = \frac{μ_{0}}{2 π} . \frac{i}{r}

(upward direction)
Net magnetic induction at O,

B = B_{1} - B_{2} = \frac{μ_{0} i}{2 r} - \frac{μ_{0}}{2 π} . \frac{i}{r}

= \frac{μ_{0} i}{2 r} [1 - \frac{1}{π}]

[downward direction]
Hence, there are no options correct.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Figure show the circular coil carrying current l kept very close but not touching at a point A on a straight conductor carrying the same current l . The magnitude of magnetic induction at the centre of the circular coil will be

Step-by-step Solution

Figure show the circular coil carrying current $l$ kept very close but not touching at a point A on a straight conductor carrying the same current $l$ . The magnitude of magnetic induction at the centre of the circular coil will be