NEETPhysicsMagnetic Effects of Current
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If the current in a circular coil is doubled and its radius is halved, the magnetic field at its centre becomes four times its original value, and its magnetic moment remains unchanged. Reason (R): The magnetic field at the centre of a circular coil is directly proportional to the current and inver
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- B(A) is false but (R) is true
- CBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- D(A) is true but (R) is false
Correct answer
B. (A) is false but (R) is true
Step-by-step solution
The magnetic field at the centre of a circular coil is B = ₀ N I 2R . Thus, B I R . The magnetic moment of a circular coil is M = N I R^2 . Thus, M I R^2 . This means Reason (R) is true. Let the new current be I' = 2I and the new radius be R' = R/2 . The new magnetic field is B' 2I R/2 = 4 ( I R ) = 4B . The magnetic field becomes four times its original value. The new magnetic moment is M' (2I) ( R 2 )^2 = 2I ( R^2 4 ) = 1 2 I R^2 = M 2 . The magnetic moment becomes half of its original value, not unchanged. There