**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 of 60

^{0} 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: m

_{e} =9.1 x 10

^{-31} kg , e=1.6 x 10

^{-19 C}
**Question 4-** A particle of mass 1x 10

^{-26 } kg and charge 1.6 x 10

^{-19 } C travelling with velocity of 1.28 x 10

^{6} m/s in +x direction enters a region having electric field E and a uniform magnetic field B such as E

_{x} =E

_{y} =0, E

_{z} = -102.4 V/m and B

_{x} =B

_{z} =0, B

_{y} =8x10

^{-2} Wb/m

^{2 } . 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} s . 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

^{-4} a

_{z} T and E=5a

_{z} V/m. A proton ( q

_{p} =1.602 x 10

^{-19} C,m

_{p} =1.6 x10

^{-27} kg) enters in the field at the origin with a velocity u

_{0} =2.5 x10

^{5} a

_{x} m/s. Describe the proton’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

^{-2}m. Find the magnetic field at the centroid of the triangle.

**Question 8-** A charge q=40 µC moves with instantaneous velocity u=(5x10

^{4})

**j **m/s through the uniform fields E=(6x10

^{4}) (.52

**i** +.56

**j **+.645

**k**) V/m , B=(1.7)(.693

**i** + .6

**j **+ .4

**k**) T 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**+0.3

**j**-0.4

**k **T such that its directed area is A=0.04

**i**-0.05

**j**+0.07

**k **m

^{2}. 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.

**Solutions **

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Class 12 Maths
Class 12 Physics