JEE Advanced 2013 · Paper 2 · Physics Q7

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PhysicsMultiple correct+3 / -1Question 7 of 60

A steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$ . This cylinder is placed coaxially inside an infinite solenoid of radius $2R$ . The solenoid has $n$ turns per unit length and carries a steady current $I$ . Consider a point $P$ at a distance $r$ from the common axis. The correct statement(s) is (are)

In the region

0<r<R

, the magnetic field is non-zero.

In the region

R<r<2R

, the magnetic field is along the common axis.

In the region

R<r<2R

, the magnetic field is tangential to the circle of radius

r

, centered on the axis.

In the region

r>2R

, the magnetic field is non-zero.

Answer and worked solution

Official answer: A, D

Fields present.

The solenoid gives a uniform axial field $\mu_0nI$ for $r<2R$ and zero outside.
The cylinder gives zero field inside ( $r<R$ ) and a circular field $\frac{\mu_0I}{2\pi r}$ outside it.

Regions.

$0<r<R$ : only the solenoid's field, nonzero. ✓
$R<r<2R$ : axial plus circular, so the net field is helical, neither purely axial nor purely tangential.
$r>2R$ : the cylinder's circular field, nonzero. ✓

(A), (D)

Topics:Ampere's circuital law

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JEE Advanced 2013 · Paper 2, Physics question 7