# Magnetic field and magnetic effects of current Problems

## Subjective Questions

Question 1
A current of 10A is flowing from east to west in a long wire kept in east-west direction. Find the magnetic field in a horizontal plane at a distance of (1) 10cm north (2) 20cm south from the wire; and in a vertical plane at a distance of (3) 30cm downward (4) 50cm upward.

Question 2
A short conductor of length 4cm is placed parallel to the long conductor of length 2m near to its centre at a distance of 2cm. The conductor carry currents of 2A and 5A respectively in opposite directions. Find the total force exert on the long conductor.

Question 3
An electron-gun G emit electron of energy 2KeV travelling in the positive X-direction. The electron are required to hit the spot S where GS= 0.1m, and the line GS makes an angle ofÂ 600Â with X-axis, as shown in the figure. A uniform magnetic field B parallel to GS exist in the region outside the electronic-gun. Find the minimum value of B needed to make the electron hit S.
Given: me =9.1 x 10-31 kg , e=1.6 x 10-19 C

Question 4
A particle of mass 1x 10-26Â Â Â kg Â and charge 1.6 x 10-19Â Â CÂ travelling with velocity of 1.28 x 106Â Â m/s Â in +x direction enters a region having electric field E and a uniform magnetic field B such asÂ Ex =EyÂ =0, EzÂ = -102.4 V/mÂ and Bx =Bz =0, By =8x10-2 Wb/m2Â Â . The particle enters this region at a long time t=0. Determine the location (x, y and z co-ordinates) of the particle at t=5x10-6 sÂ . If the electric field switched off at this instant (with the magnetic field still present), what will be the position of the particle at t=7.46 x10-6 s.

Question 5
In a certain region surrounding the origin of the coordinates, B=5 x10-4Â  az TÂ Â and E=5az V/m. A proton ( qp =1.602 x 10-19Â  C,mpÂ  =1.6 x10-27Â  kg) enters in the field at the origin with a velocity u0 =2.5 x105Â  ax m/s. Describe the protonâ€™s motion and give its position after three complete revolutions

Question 6
Find an expression for magnetic field at the centre of a circular current carrying loop.

Question 7
A current of 1.0 A is flowing in the sides of an equilateral triangle of sides 4.5 x 10-2m. Find the magnetic field at the centroid of the triangle.

Question 8
A charge q=40 ÂµCÂ Â moves with instantaneous velocity u=(5x104)Â  jÂ m/sÂ through the uniform fieldsÂ Â  E=(6x104) (.52 iÂ  +.56j +.645 k) V/mÂ , B=(1.7)(.693 iÂ + .6 j + .4k) TÂ find the magnitude and direction of the instantaneous force on q.

Question 9
Find the force on each segment of the wire as shown below in the figure

if B=0.15T. Assume that the current in the wire is 5A.

Question 10
A planar coil of 12 turns carries 15A. The coil is oriented with respect to the uniform magnetic field B=0.2i+0.3j-0.4k T such that its directed area is A=0.04i-0.05j+0.07k m2. Find (a) the dipole moment of the coil (b)the potential energy of the in the given orientation, and (c)the angle between the positive normal to the coil and the field.

## Objective Type questions

Question 11
A wire in the form of semicircle of radius r lies on the top of a smooth table . A downward directed uniform magnetic field of magnitude B is confined to region above the dashed line in the below figure.

The ends of the semicircle are attached to springs C and D whose other ends are fixed. The current i is introduced by attaching a battery to the ends of the springs as shown above.
Let $T_1$ be the tension in the Spring C and $T_2$ be the tension in the spring D
Which of the one following is true
(a) $T_1 + T_2 = 2iBr$
(b) $T_1 - T_2 = 2iBr$
(c) $T_1 + T_2 = iBr$
(d) None of these

Question 12
Find the torque which acts on the rectangular current loop as shown in below figure

The magnetic field is given by
$\mathbf{B}=B_0 \mathbf{i}$
(a) $iAB \cos \theta \mathbf{j}$
(b) $iAB \sin \theta \mathbf{j}$
(c) $-iAB \cos \theta \mathbf{j}$
(d) $-iAB \sin \theta \mathbf{j}$

Question 13
Find the force on the triangular loop ABC as shown in figure near an infinite straight wire. Both the loop and the wire carry a steady current I.

## Paragraph Based Questions

Find the magnetic dipole moment of the bookend shaped loop as shown in below figure. All the sides has length b and it carries a current I

Question 14
Find the magnetic dipole moment of the loop
(a) $Ib^2(\mathbf{j}+\mathbf{k})$
(b) $Ib^2(\mathbf{j}-\mathbf{k})$
(c) $Ib^2(\mathbf{i}+\mathbf{k})$
(d) $Ib^2(\mathbf{i}+\mathbf{j})$
Question 15
If a uniform magnetic field exists in the region
$B=B_0(\mathbf{i}+\mathbf{j})$
Find the torque acting on the loop
(a) $ib^2B_0(\mathbf{j}+\mathbf{k}-\mathbf{i})$
(b) $ib^2B_0(\mathbf{j}-\mathbf{k}+\mathbf{i})$
(c) $ib^2B_0(\mathbf{k}-\mathbf{i})$
(d) $ib^2B_0(\mathbf{j}-\mathbf{k}-\mathbf{i})$

## Match the column

Question 16 A long straight metal rod of Radius $R_1$ has a very large hole of radius $R_2$ drilled parallel to the rod axis. The rod is carrying current I .The cross-section of the rod from the top is shown below

The distance between C and A is 3d
Column A
(P) Magnetic field at Point A
(Q) Magnetic field at Point B
(R) Magnetic field at point C

Column B

Question 17 A charged particle would continue to move with a constant velocity in a region wherein,
(a) $\mathbf{E} = 0$, $\mathbf{B} \ne 0$
(b) $\mathbf{E} \ne 0$, $\mathbf{B} \ne 0$
(c) $\mathbf{E} \ne 0$, $\mathbf{B} = 0$
(d) $\mathbf{E} = 0$, $\mathbf{B} \ne 0$