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QPages 249-253: Q36: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q36 Solution: Two circular coils of radii 5.0 cm and 10 cm carry equal…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often add the magnitudes of the two coil fields without assigning a sign based on the right‑hand rule; when the currents are opposite the fields must be subtracted as vectors, not just their absolute values. Remember to give each term a positive or negative sign according to its direction before combining them.

Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centres coincide. Find the magnitude of the magnetic field

B

at the common centre of the coils if the currents in the coils are a) in the same sense b) in the opposite sense.

Step-by-Step Verified Solution

**Answer:** (a)

B = 1.88 \times 10^{-3}

T (b)

B = 6.28 \times 10^{-4}

T. **Step-by-Step Explanation:** Coil 1:

r_1 = 5

cm,

N_1 = 50

; Coil 2:

r_2 = 10

cm,

N_2 = 100

.

i = 2

A. (a) Same sense:

B = \frac{\mu_0 N_1 i}{2r_1} + \frac{\mu_0 N_2 i}{2r_2} = 1.88 \times 10^{-3}

T. (b) Opposite sense:

B = \frac{\mu_0 N_2 i}{2r_2} - \frac{\mu_0 N_1 i}{2r_1} = 6.28 \times 10^{-4}

T.

All Questions in this Chapter

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