A steady current 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 . Consider a point

Question

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): [2013]

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(1, 4)

In the region $I$ , the net magnetic field is due to the current in the solenoid.

In the region $r > 2 R$ , the magnetic field is present due to the current in the cylinder.

For the region $R < r < 2 R$ , the magnetic field is neither along the common axis, nor tangential to the circle of radius $r$ .

Solution

1 In the region $0 < r < R$ , the magnetic field is non-zero.

2 In the region $R < r < 2 R$ , the magnetic field is along the common axis.

3 In the region $R < r < 2 R$ , the magnetic field is tangential to the circle of radius $r$ , centered on the axis.

4 In the region $r > 2 R$ , the magnetic field is non-zero.

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Solution

1 In the region 0<r<R, the magnetic field is non-zero.

2 In the region R<r<2R, the magnetic field is along the common axis.

3 In the region R<r<2R, the magnetic field is tangential to the circle of radius r, centered on the axis.

4 In the region r>2R, the magnetic field is non-zero.

Ans. (1, 4) In the region 0<r<R, the net magnetic field is due to the current in the solenoid. In the region r>2R, the magnetic field is present due to the current in the cylinder. For the region R<r<2R, the magnetic field is neither along the common axis, nor tangential to the circle of radius r.

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1 In the region $0 < r < R$ , the magnetic field is non-zero.

2 In the region $R < r < 2 R$ , the magnetic field is along the common axis.

3 In the region $R < r < 2 R$ , the magnetic field is tangential to the circle of radius $r$ , centered on the axis.

4 In the region $r > 2 R$ , the magnetic field is non-zero.