# 5.Magnetic Fields due to Currents( with Answers)

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1 5.Magnetic Fields due to Currents( with Answers) 1. Suitable units for µ. Ans: TmA -1 ( Recall magnetic field inside a solenoid is B= µ ni. B is in tesla, n in number of turn per metre, I is current in amperes. B T µ = = = TmA 1 ni m A 1 2. Electrons are going around a circle in a counter clockwise direction. At the centre of the circle they produce a magnetic field that is. A negatie charge circulating in counter clockwise direction is equialent to a positie charge in clockwise direction. So using thumb rule we can say magnetic field is downwards, into the page. 3. Explain why is there no magnetic field when a wire is simply doubled back on itself. The magnetic field due to the two wires will be in opposite direction. So they will cancel each other out. 4. The magnitude of the magnetic field at point P, at the centre of the semicircle shown, is gien by. Magnetic field at the centre of a circular coil is haled to obtain the magnetic field due to a semi-circle. This is correct since the contribution due to each small element is added up to find the magnetic field due to the full coil. To find the field due to the semi circle the magnetic field due to a small element will be integrated oer half the length. µ i B = 4R

2 5. A wire carrying a large current i from east to west is placed oer an ordinary magnetic compass. The end of the compass needle marked N will point. The compass needle will point towards south. 6. Draw magnetic field lines around the coil. 7. Two long parallel straight wires carry equal currents in opposite directions. At a point midway between the wires, the magnetic field they produce is. Zero as the field due to current in opposite directions cancel each other out. 8. Two parallel wires carrying equal currents of 1A attract each other with a force 1mN. If both currents are doubled, the force of attraction will be. The force will become 4 times as Force per unit length is, f ii 1 2 = µ 2πr

3 9. In Ampere s law B.ds r r = µ i, the integration must be oer. A closed loop 1. The magnetic field B inside a long ideal solenoid depends on. B = µ ni so the magnetic field depends on the number of turns per unit length, the current through the solenoid and permeability of medium within the solenoid. For instance if an iron core is placed inside the solenoid the permeability will increase so the magnetic field will also increase. 11. A solenoid is 3. cm long and has a radius of.5 cm. It is wrapped with 5 turns of wire carrying a current of 2. A. The magnetic field in tesla at the centre of the solenoid is. 7 5 B = µ ni = 4π 1 2T Draw the magnetic field lines inside the solenoid for current shown below: 13. If R is the distance from a magnetic dipole, then the magnetic field it produces is proportional to. It is proportional to 1/R Two parallel wires, 4 cm apart, carry currents of 2 A and 4 A respectiely, in the same direction. The force per unit length is N/m of one wire on the other is. B = 7 4π π A loop of current-carrying wire has a magnetic dipole moment of A.m 2. The moment initially makes an angle of 9 with a.5 T magnetic field. As it turns to become aligned with the field, the work done by the field is. U = mb cosθ Work mb mb done = cos 9 ( cos ) 4 =mb = J

4 16. The units of magnetic dipole moment are. Am A current of 3. A is clockwise around the outside edge of this page, which has an area of m 2. The magnetic dipole moment is. m = IA = A m 2 2 (3. )(5.8 1 ) 18. A cyclotron operates with a gien magnetic field and at a gien frequency. If R denotes the radius of the final orbit, the final particle energy is proportional to. 2 m = qb r qbr = m qbr q B r KE = m = m = m m 2 2 The final kinetic energy of the particle will depend on its charge to mass ratio, magnetic field and radius of the orbit. 19. A proton, traelling perpendicular to a magnetic field, experiences the same force as an alpha particle which is also traelling perpendicular to the same field. Find the ratio of their speeds p p proton alpha q B = q B proton alpha q a a alpha = = q proton An electron moes in the negatie x direction through a uniform magnetic field in the negatie y direction. The magnetic force on the electron is along. Force is along xb ( cross B) so it will be along z direction. 21. State Biot-Saart Law. 22. What are the SI units of a) magnetic field b) flux c) µ π 4 Ans a) tesla T b) weber Wb c) T.m/A

5 23. Define magnetic field lines. The direction of the tangent to the magnetic field line gies the direction of the magnetic field at that point. The spacing of the lines represents the magnitude of the magnetic field, they are closely spaced where the field is strong and conerse. 24. Derie the expression for the magnetic field due to long straight current carrying wire. From the expression for the magnetic field, state the direction of the field lines. Take a small element of the wire. Write the magnetic field due to it at a distance r from the wire. Then integrate it to find the magnetic field due to the entire wire. The direction of the field lines can be drawn as shown in the figure. 25. Derie the expression for the magnetic field due to a current carrying circular loop. From the expression, derie the field at large distances from the loop and at the center of the loop. The magnetic field due to a small element of the loop is written using Biot-Saart s law. Then the total field is obtained by integrating oer the loop. At large distances from the loop the field is like the field due to a magnetic dipole, if the distance is measured along the axis of the loop, the field will be µ 2m 3 4π r Here m is the dipole moment and r is the distance from the centre of dipole 26. State Fleming s left-hand rule. Stretch the thumb, forefinger and middle finger of your left hand such that they are mutually perpendicular. If the first finger points in the direction of magnetic field and the second finger in the direction of current, then the thumb will point in the direction of motion or force acting on the conductor. 27. Write the expression for the force between 2 short parallel current carrying wires separated by a distance much larger than their length. To find force, find magnetic field at one wire due to current in other wire. Now you are placing the second current carrying wire in a magnetic field due to the first wire. This wire will now experience a force gien by F = i l x B. Force per unit length is, f ii 1 2 = µ 2πr

6 28. Fill in the blanks a) Force between two parallel current carrying wires is.attractie b) Force between 2 anti-parallel current carrying conductors.repulsie c) Lorentz force is.q x B d) Ampere s circuital law is the line integral of _magnetic field around any closed circuit is equal to _ µ times the _current threading on passing through this circuit. e) Magnetic field for a straight solenoid n turns per unit length is _ µ ni. f) Units of magnetic dipole moment m is _Am 2. g) The direction of the magnetic moment is gien as follows: If the current in the circular loop is directed along the cured fingers of the hand, the magnetic moment is directed along the thumb sticking out. h) The torque on a magnetic dipole m in a uniform field B is gien as _m x B. i) Current sensitiity of a moing coil galanometer is defined as _ I φ. j) Voltage sensitiity of a moing coil galanometer is defined as _ V φ. k. In the cyclotron resonance condition, the frequency ω is qb m. 29. Describe the principle and working of a moing coil galanometer. A current carrying coil is placed in a uniform radial magnetic field. It is mounted so that it can rotate about an axis. For any orientation of the coil, the net magnetic field through the coil is perpendicular to the normal ector of the coil, or parallel to the plane of the coil. A spring proides a counter torque that balance the rotating torque, so that a steady current I in the coil will cause a steady deflection φ. The more the current, the more the deflection in the coil. NiAB sinθ = κφ NiAB sinθ φ = κ 3. Derie the expression for the path followed by a moing charged particle in a uniform magnetic field. What is the (i) radius of the path for an electron (ii) frequency of the reolution of the electron 2 m 1) = qb r qbr = m m r = qb qb 2) w = = r m

7 Please let me know if you find any typing errors or other errors.

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