# Numericals » 09-Numerical Problems

## “Magnetism” Numerical Problems

Try to solve the following “Magnetism & Magnetic Effect of Current” numerical problems to clear the concepts in solving the numerical problems.

First of all go to the theory portion of the respective topic and then try to solve the numerical problems by yourself. If facing problem in solving the numerical, click on the Go to solution button to see the ready made solution placed at the bottom of each numerical problem.

### 01. PROBLEM – P090101

A magnetized wire of length ( 8 \ cm ) has a magnetic moment of ( 80 \times 10^{-3} J \ T^ {-1} ) . It is then bent into a semi-circular arc. Find the pole strength. What is the magnetic moment in terms of ( \pi ) ?

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### 02. PROBLEM – P090102

Two identical thin bar magnets, each of length ( L ) , and pole strength ( q_{m} ) are placed at right angles to each other, with N pole of one magnet touching the south pole of the other. Find the magnetic moment of the system.

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### 03. PROBLEM – P090103

At a certain place, a compass points 13 \degree \ W of geographical north. If the dip at that place is 60 \degree and magnetic field is ( 0.16 \ G ) . Find the earth’s field at that place.

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### 04. PROBLEM – P090104

A long solenoid having 5000 turns / m carries a current of ( 2.0 \ A ) . Calculate (i) magnetic flux density at the centre of the solenoid.

Now, an iron rod is inserted in the solenoid. Calculate (i) magnetic intensity and (ii) magnetic flux density at the centre of the solenoid. Given, magnetic susceptibility of iron is ( 5 \times 10^{3} ) .

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### 05. PROBLEM – P090105

Calculate permeability and susceptibility of a magnetic bar of cross section ( 0.1 \ cm^2 ) having magnetic flux of ( 2.41 \times 10^{-5} ) weber due to magnetic intensity of ( 3200 \ Am^{-1} )

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### 06. PROBLEM – P090106

Find (a) the magnetization ( I ) (b) the magnetic intensity ( H ) and (c) the magnetic field ( B ) at the centre of a bar magnet having pole strength ( 3.6 \ Am ) , magnetic length ( 12 \ cm ) and cross sectional area ( 0.9 \ cm^2 ) .

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### 07. PROBLEM – P090107

A magnetic needle of length ( 10 \ cm ) , suspended at its middle point through a thread, stays at an angle of 45 \degree with the horizontal. The horizontal component of the earth’s magnetic field is ( 18 \ \mu T ) . (a) Find the vertical component of this field. (b) If the pole strength of the needle is ( 1.6 \ Am ) , what vertical force should be applied to an end so as to keep it in horizontal position?

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### 08. PROBLEM – P090108

A magnetic needle having magnetic moment ( 10 \ Am^2 ) and length ( 2.0 \ cm ) is clamped at its centre in such a way that it can rotate in the vertical east-west plane. A horizontal force towards east is applied at the north pole to keep the needle fixed at an angle of 30 \degree with the vertical. Find the magnitude of the applied force. The vertical component of the earth’s magnetic field is ( 40 \mu T ) .

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### 09. PROBLEM – P090109

A proton and an ( \alpha ) particle enter a uniform magnetic field perpendicular to Y axis with the same speed. If proton takes ( 25 \ \mu s ) to make 5 revolutions, then what will be the time period for the ( \alpha ) particle?

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### 10. PROBLEM – P090110

In a cyclotron, if a deuteron can gain an energy of ( 40 \ MeV ) , then what will be the energy of a proton?

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### 11. PROBLEM – P090111

A current ( i ) flows in the network shown in the figure. Find resulting magnetic induction at point P .

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### 12. PROBLEM – P090112

An infinitely long conductor is bent into shape as shown in figure. The semicircular part lies in YZ plane, while one part is along X axis and the other is parallel to Y axis at a distance ( R ) from it. If current ( I ) flow through the conductor, find magnetic field at the centre C of the semicircular part.

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### 13. PROBLEM – P090113

A galvanometer of resistance ( 50 \ \Omega ) gives full scale deflection for a current of ( 0.05 \ A ) . Calculate the length of shunt wire required to convert the galvanometer into an ammeter of range ( 0.5 \ A ) . The diameter of the shunt wire is ( 2 \ mm ) and its resistivity is ( 5 \times 10^{-7} \ \Omega \ m ) .

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### 14. PROBLEM – P090114

A galvanometer with a resistance of ( 12 \ \Omega ) gives full scale deflection for a current of ( 0.0025 \ A ) . What is the net resistance of the meter when it is converted into an ammeter to read ( 7.5 \ A ) and also when it is converted into a voltmeter to read ( 10 \ V ) ?

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### 15. PROBLEM – P090115

A wire is bent in the form of an equilateral triangle \triangle PQR of side ( 10 \ cm ) and carries a current of ( 5.0 \ A ) . It is placed in a magnetic field ( \overrightarrow {B} ) of magnitude ( 2.0 \ T ) directed perpendicularly to the plane of the loop. Find the forces on the three sides of the triangle.

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1. Magnetic force on a current carrying conductor.

### 16. PROBLEM – P090116

A rectangular coil of size ( 3.0 \ cm \times 4.0 \ cm ) and having 100 turns, is pivoted about the Z axis as shown in figure.

The coil carries an electric current of ( 2.0 \ A ) and a magnetic field of ( 1.0 \ T ) is present along the Y axis. Find the torque acting on the coil if the side in the X Y plane makes an angle ( \theta = 37 \degree ) with the X axis as shown in figure.

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