#### Biot-Savart’s Law and Ampere’s Law problems and answers:

**Ques:** If a copper rod carries a direct current, the magnetic field associated with the current will be

(a) Only inside the rod

(b) Only outside the rod

(c) Both inside and outside the rod

(d) Neither inside nor outside the rod

**Ques:** When a certain length of wire is turned into one circular loop, the magnetic induction at the centre of coil due to some current flowing is B_{1} If the same wire is turned into three loops to make a circular coil, the magnetic induction at the center of this coil for the same current will be

(a) B_{1}

(b) 9B_{1
}(c) 3B_{1}

(d) 27B_{1}

**Ques:** A circular coil ‘*A*’ has a radius *R* and the current flowing through it is *I*. Another circular coil ‘*B*’ has a radius 2*R *and if 2*I* is the current flowing through it, then the magnetic fields at the centre of the circular coil are in the ratio of (*i.e.B _{A}
*

*to B*

_{B})

(a) 4 : 1

(b) 2 : 1

(c) 3 : 1

(d) 1 : 1

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**Ques:** The current in the windings on a toroid is 2.0*A*. There are 400 turns and the mean circumferential length is 40*cm. *If the inside magnetic field is 1.0*T*, the relative permeability is near to

(a) 100

(b) 200

(c) 300

(d) 400

**Ques:** The magnetic induction at any point due to a long straight wire carrying a current is

(a) Proportional to the distance from the wire

(b) Inversely proportional to the distance from wire

(c) Inversely proportional to the square of the distance from the wire

(d) Does not depend on distance

**Ques:** A magnetic field can be produced by

(a) A moving charge

(b) A changing electric field

(c) None of these

(d) Both of these

**Ques:** A current *I* flows along the length of an infinitely long, straight and thin-walled pipe. Then

(a) The magnetic field at all points inside the pipe is the same but not zero

(b) The magnetic field at any point inside the pipe is zero

(c) The magnetic field is zero only on the axis of the pipe

(d) The magnetic field is different at different points inside the pipe

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**Ques:** The direction of magnetic lines of force produced by passing a direct current in a conductor is given by

(a) Lenz’s law

(b) Fleming’s left hand rule

(c) Right hand palm rule

(d) Maxwell’s law

**Ques:** Due to 10 *ampere* of current flowing in a circular coil of 10 *cm* radius, the magnetic field produced at its centre is 3.14 x 10^{–3} Weber / m^{2}. The number of turns in the coil will be

(a) 5000

(b) 100

(c) 50

(d) 25

**Ques:** When the current flowing in a circular coil is doubled and the number of turns of the coil in it is halved, the magnetic field at its centre will become

(a) Four times

(b) Same

(c) Half

(d) Double

**Ques:** Two infinitely long parallel wires carry equal current in same direction. The magnetic field at a mid point in between the two wires is

(a) Twice the magnetic field produced due to each of the wires

(b) Half of the magnetic field produced due to each of the wires

(c) Square of the magnetic field produced due to each of the wires

(d) Zero

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**Ques:** The direction of magnetic lines of forces close to a straight conductor carrying current will be

(a) Along the length of the conductor

(b) Radially outward

(c) Circular in a plane perpendicular to the conductor

(d) Helical

**Ques:** Field inside a solenoid is

(a) Directly proportional to its length

(b) Directly proportional to current

(c) Inversely proportional to total number of turns

(d) Inversely proportional to current

**Ques:** 20 *ampere* current is flowing in a long straight wire. The intensity of magnetic field at a distance 10 *cm* from the wire will be

(a) 4 ´ 10^{–5} *Wb/m*^{2}

(b) 9 ´ 10^{–5} *Wb/m*^{2
}(c) 8 ´ 10^{–5} *Wb/m*^{2}

(d) 6 ´ 10^{–5} *Wb/m*^{2}

**Ques:** A neutral point is obtained at the centre of a vertical circular coil carrying current. The angle between the plane of the coil and the magnetic meridian is

(a) 0

(b) 45°

(c) 60°

(d) 90°

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**Ques:** The magnetic induction at the centre of a current carrying circular of coil radius *r*, is

(a) Directly proportional to* r*

(b) Inversely proportional *r
*(c) Directly proportional to

*r*

^{2}

(d) Inversely proportional to

*r*

^{2}

**Ques:** An electric current passes through a long straight wire. At a distance 5 *cm *from the wire, The magnetic field is *B*. The field at 20 *cm * from the wire would be

(a) B/6

(b) B/4

(c) B/3

(d) B/2

**Ques:** The magnetic field at the centre of a circular coil of radius *r* carrying current *I* is B_{1}. The field at the centre of another coil of radius 2 *r *carrying same current *I *is B_{2}. The ratio B_{1}/B_{2} is

(a) ½

(b) 1

(c) 2

(d) 4

**Ques:** A long solenoid of length *L* has a mean diameter *D. *It has n layers of windings of* N *turns each. If it carries a current ‘*i*’ the magnetic field at its centre will be

(a) Proportional to *D
*(b) Inversely proportional to

*D*

(c) Independent of

*D*

(d) Proportional to

*L*

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**Ques:** The magnetic field near a current carrying conductor is given by

(a) Coulomb’s law

(b) Lenz’ law

(c) Biot-savart’s law

(d) Kirchoff’s law

**Ques:** Two concentric coplanar circular loops of radii r_{1} and r_{2} carry currents of respectively i_{1} and i_{2} in opposite directions (one clockwise and the other anticlockwise.) The magnetic induction at the centre of the loops is half that due to i_{1} alone at the centre. If r_{2} = 2r_{1} the value of i_{2}/i_{1} is

(a) 2

(b) ½

(c) ¼

(d) 1

**Ques:** Magnetic fields at two points on the axis of a circular coil at a distance of 0.05*m* and 0.2*m* from the centre are in the ratio 8 : 1. The radius of the coil is

(a) 1.0 *m
*(b) 0.1

*m*

(c) 0.15

*m*

(d) 0.2

*m*

**Ques:** A current carrying wire in the neighborhood produces

(a) No field

(b) Electric field only

(c) Magnetic field only

(d) Electric and magnetic fields

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**Ques:** A long straight wire carrying current of 30*A* is placed in an external uniform magnetic field of induction 4 x 10^{–4}*T. *The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in *tesla *at a point 2.0 cm away from the wire is

(a) 10^{–4}

(b) 3 x 10^{–4
}(c) 5 x 10^{–4}

(d) 6 x 10^{–4}