**Moving Charges and Magnetism** **Important Questions for CBSE Class 12 Physics Magnetic Field Laws and their Applications**

**1.**The space in the surroundings of a magnet or a current-carrying conductor in which its magnetic influence can be experienced is called magnetic field. Its SI unit is Tesla (T).

**2.Oersted** experimentally demonstrated that the current-carrying conductor produced magnetic field around it.

**Previous Year Examination Questions**

**1 Mark Question**

**1.Draw the magnetic field lines due to a current carrying loop. [Delhi 2013 C]**

**Ans.**

**2 Marks Questions**

**2.Considering the case of a parallel plate capacitor being charged, show how one is required to generalise Ampere’s circuital law to include the term due to displacement current. [All India 2014,2011]**

**Ans.**

**3.(i) State Biot-Savart’s law in vector form expressing the magnetic field due to an element dl carrying current 7 at a distance r from the element.**

** (ii) Write the expression for the magnitude of the magnetic field at the centre of a circular loop of radius r carrying a steady current 7. Draw the field lines due to the current loop.[All India 2014C]**

**Ans.(i) **

**(ii)**

**4.Define one tesla using the expression for the magnetic force acting on a particle of charge q moving with velocity v in a magnetic field B. [Foreign 2014]**

** Ans.**

**5.Two identical circular loops P and Q, each of radius r and carrying equal currents are kept in the parallel planes having a common axis passing through O. The direction of current in P is clockwise and in Q is anti-clockwise as seen from O which is equidistant from the loops P and Q. Find the magnitude of the net magnetic field at O.**

** **

**Ans.**

**6.A circular coil of closely wound N turns and radius r carries a current 7. Write the expressions for the following:**

** (i)The magnetic field at its centre.**

** (ii)The magnetic moment of this COil. [All India 2012]**

**Ans.**

**7.A particle of charge q and mass m is moving with velocity It is subjected to a uniform magnetic field B directed perpendicular to its velocity. Show that it describes a circular path. Write the expression for its radius.[Foreign 2012]**

**Ans**.

**Ans.**

**9.A long solenoid of length L having N turns carries a current I.Deduce the expression for the magnetic field in the interior of the solenoid. [All India 2008; 2011C]**

**Ans.**

where number of turns per unit length. This is required expression for magnetic field inside the long current carrying solenoid.

**10.Obtain with the help of a necessary diagram, the expression for the magnetic field in the interior of a toroid carrying current. [HOTS; All India 2011C]**

**Ans.**

**11.A straight wire of length L is bent into a semi-circular loop. Use Biot-Savart’s law to deduce an expression for the magnetic field at its centre due to the current 7 passing through it. [Delhi 2011c]**

**Ans.**

**12.State Ampere’s circuital law. Show through an example, how this law enables an easy evaluation of the magnetic field when there is a symmetry in the system? [All India 2010]**

**Ans.**

**13.State Biot-Savart’s law. A current I flows in a conductor placed perpendicular to the plane of the paper. Indicate the direction of the magnetic field due to a small element dl at a point P situated at a distance r from the element as shown in the figure.[Delhi 2009]**

** **

**Ans.**

**14.A wire of length L is bent round in the form of a coil having N turns of same radius. If a steady current I flows through it in clockwise direction, then find the magnitude and direction of the magnetic field produced at its centre.[Foreign 2009]**

**Ans.**

**Ans.**

**16.Using Ampere’s circuital law,obtain an expression for the magnetic field along the axis of a current carrying solenoid of length / and having N number of turns. [All India 2008]**

**Ans.**

**17.A circular coil of radius R carries a current /. Write the expression for the magnetic field due to this coil at its centre. Find out the direction Of the field. [All India 2008 C]**

**Ans.**

**3 Marks Questions**

**18.(i) State Ampere’s circuital law expressing it in the integral form, (ii) Two long co-axial insulated solenoids and S _{2} of equal length are wound one over the other as shown in the figure.A steady current / flows through the inner solenoid S_{x} to the other end B which is connected to the outer solenoid through which the some current / flows in the opposite direction so, as to come out at end A. If n_{x} and n_{2} are the number of turns per unit length, find the magnitude and direction of the net magnetic field at a point**

**(a)inside on the axis and**

**(b)outside the combined system**

**Ans.**

**19.(i) How is a toroid different from a solenoid?**

** (ii) Use Ampere’s circuital law to obtain the magnetic field inside a toroid.**

** (iii)Show that in an ideal toroid the ^{1} magnetic field (a) inside the toroid and (b) outside the toroid at any point in the open space is zero. [All India 2014 C]**

**Ans.**(i) A toroid can be viewed as a solenoid which has been bent into circular shape to close on itself.

(ii)

(iii)For the evaluation of magnetic field for a symmetrical system, we can consider the example of a current carrying solenoid. Now,

where number of turns per unit length. This is required expression for magnetic field inside the long current carrying solenoid.

**Ans.**

**Ans.**

**22.A solenoid of length 1.0 m has a radius of 1 cm and has a total of 1000 turns wound on it. It carries a current of 5 A. Calculate the magnitude of the axial magnetic field inside the solenoid. If an electron was to move with a speed of 10 ^{4} m/s along the axis of this current carrying solenoid, what would be the force experienced by this electron? [Delhi 2008 C]**

**Ans.**

**23.A long straight wire of a circular cross-section of radius a carries a steady current /. The current is uniformly distributed across the cross-section of the wire. Use Ampere’s circuital law to show that the magnetic field due to this wire in the region inside the wire increases in direct proportion to the distance of the field point from the axis of the wire. Write the value of this magnetic field on the surface of the wire.[All India 2008 C]**

**Ans. **

**5 Marks Questions**

**24.Two very small identical circular loop(1) and (2) carrying equal current I are placed vertically (with respect to the plane of the paper) with their geometrical axes perpendicular to each other as shown in the figure. Find the magnitude and direction of the net magnetic field produced at the point O.[Delhi 2014]**

** **

**Ans.**

**Ans.. **

(i)Let us consider a circular loop of radius a with centre C. Let the plane of the coil be perpendicular to the plane of the paper and current / be flowing in the direction shown. Suppose P is any point on the axis at direction r from the centre.

Now, consider a current element **Idl** on top L, where current comes out of paper normally, whereas at bottom **M** enters into the plane paper normally

**26.State Biot-Savart’s law and give the mathematical expression for it. Use law to derive the expression for the magnetic field due to a circular coil carrying current at a point along its axis. How does a circular loop carrying current behave as a magnet?[Delhi 2011]**

**Ans.**For Biot-Savart’s law

For the magnetic field due to a circular coil carrying current at a point along its axis

**(i)**Let us consider a circular loop of radius a with centre C. Let the plane of the coil be perpendicular to the plane of the paper and current / be flowing in the direction shown. Suppose P is any point on the axis at direction r from the centre.

Now, consider a current element **Idl** on top L, where current comes out of paper normally, whereas at bottom **M** enters into the plane paper normally

As current carrying loop has the magnetic held lines around it which exists a force on a moving charge. Thus, it behaves as a magnet with two mutually opposite poles

The anti-clockwise flow of current behaves like a North pole, whereas clockwise flow as South pole. Hence, loop behaves as a magnet

**27.(i) Using Ampere’s circuital law, obtain the expression for the magnetic field due to a long solenoid at a point inside the solenoid on its axis.**

** (ii) In what respect, is a toroid different from a solenoid? Draw and compare the pattern of the magnetic field lines in the two cases.**

** (iii) How is the magnetic field inside a given solenoid made strong?[All India 2011]**

**Ans.(i)**

where, n = number of turns per unit length. This is required expression for magnetic field inside the long current carrying solenoid.

(ii) Solenoid is a hollow circular ring having large number of turns of insulated copper wire on it.

Therefore, we can assume that toroid is a bent solenoid to close on itself.

The magnetic fields due to solenoid and toroid is given in figures below

Magnetic field inside the solenoid is a uniform, strong and along its axis also field lines are all most parallel while inside the toroid field line makes closed path.

(iii) The magnetic field in the solenoid can be increased by inserting a soft iron core inside it.

**28.(i) State Ampere’s circuital law.**

** (ii) Use it to derive an expression for magnetic field inside along the axis of an air cored solenoid.**

** (iii) Sketch the magnetic field lines for a finite solenoid. How are these field lines different from the electric field lines from an electric dipole? [Foreign 2010]**

**Ans.(i)**For statement of Ampere’s circuital law

(ii)

where, n = number of turns per unit length. This is required expression for magnetic field inside the long current carrying solenoid.

**29.(i)Using Biot-Savart’s law, deduce an expression for the magnetic field on the axis of a circular current carrying loop.**

** (ii) Draw the magnetic field lines due to a current carrying loop.**

** (iii) A straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 2.0 cm as shown in the figure. What is the magnetic field B at O due to**

** (a)straight segments,**

** (b)the semi-circular arc?[Foreign 2010]**

** **

**Ans.(i)**Let us consider a circular loop of radius a with centre C. Let the plane of the coil be perpendicular to the plane of the paper and current / be flowing in the direction shown. Suppose P is any point on the axis at direction r from the centre.

Now, consider a current element **Idl** on top L, where current comes out of paper normally, whereas at bottom **M** enters into the plane paper normally

**30.(i) State Ampere’s circuital law. Show through an example, how this law enables an easy evaluation of this magnetic field when there is a symmetry in the system?**

** (ii) What does a toroid consist of? Show that for an ideal toroid of closely wound turns, the magnetic field.**

** (a)inside the toroid is constant.**

** (b)in the open space inside an exterior to the toroid is zero.[All India 2010 C]**

**Ans.**(i) For statement of Ampere’s law

For the evaluation of magnetic field for a symmetrical system, we can consider the example of a current carrying solenoid. Now,

where, n = number of turns per unit length. This is required expression for magnetic field inside the long current carrying solenoid.

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