# Numerical Problems : Magnetic Effect Of Current

#### LEVEL – I

Q:1. Two straight infinitely long and thin parallel wires are spaced 0.1 m apart and carry a current of 10 ampere each. Find the magnetic field at a point which is at a distance of 0.1 m from both wires in the two cases when the currents are in the (a) same and (b) opposite directions (Given μo = 4π × 10-7 Tm/A).

Ans: (a) 3.46 × 10-5 Tesla (b) 2 × 10-5 Tesla

Q:2. A beam of protons with a velocity 4 × 105 m/sec enters a uniform magnetic field of 0.3 Tesla at an angle of 60° to the magnetic field. Find the radius of the helical path taken by the proton beam. Also find the pitch of the helix , which is the distance travelled by a proton in the beam parallel to the magnetic field during one period of rotation. [ Mass of proton = 1.67 × 10-27 Kg , charge on proton = 1.6 × 10-19 C ]

Ans: r = 1.205 × 10-2 m ; Pitch of the helix = 4.4 cm

Q:3. A long horizontal wire P carries a current of 50 A. It is rigidly fixed. Another fine wire Q is placed directly above and parallel to P. The weight of wire Q is 0.075 N/m and carries a current of 25 A. Find the position of wire Q from P so that the wire Q remains suspended.

Ans: 3.33 mm

Q:4. A circular coil of average radius 6 cm has 20 turns. A current of 1.0 A passes through it. Calculate the magnetic induction at
(a) the centre of the coil
(b) at a point on the axis 8 cm away from the centre.

Ans: (a) 2.09 × 10-4 T (b) 4.5 × 10-5 T

Q:5. (a) A proton is moving in a magnetic field. The field is into the plane of the page. The velocity vector lies in the plane of the page, perpendicular to . Describe the motion of proton.

(b) In part (i) , if the radius of the circle is 0.5 m and the magnitude of the magnetic field is 1.2 Wbm-2 , find the frequency of revolution and the kinetic energy of the proton.
Charge of the proton = 1.6× 10-19 C . Mass of the proton=1.67 × 10-27 kg.

Ans : 1.83 x 107 Hz ; K.E = 17.2 MeV

Q:6. In the framework of wires shown in figure, a current of i amperes is allowed to flow. Calculate the magnetic induction at the centre O. If angle α is equal to 90°, then what will be the value of magnetic induction at O ?

Ans: $\displaystyle \frac{\mu_0 i}{8} (\frac{3}{R_1} + \frac{1}{R_2})$

Q:7. A loop of flexible conducting wire of length 0.5 m lies in a magnetic field of 1.0 T perpendicular to the plane of the loop. Show that when a current is passed through the loop, it opens into a circle. Also calculate the tension developed in the wire if the current is 1.57 amp.

Ans: 0.125 N

Q:8. A beam of protons move undeviated through a region of space having uniform transverse electric and magnetic fields. These fields are mutually perpendicular and their values are 120 k v/m and 50 mT respectively. If this beam strikes a grounded target , then what will be the force exerted by the beam on the larger. Given that beam current is equal to I = 0.8 mA and mass of the proton = 1.673 x 10-27 kg.

Ans: 2 × 10-5 N

Q:9. A wire is bent in the form of a circular arc with a straight portion AB. If current flowing in the wire is i, find the magnetic induction at the centre O.

Ans: $\displaystyle \frac{\mu_0 i}{2 \pi R}(\pi -\phi + tan\phi)$

Q:10. Show that the force on a wire between a and b of arbitrary shape of figure is the same as force on the straight wire between the same two points when they carry the same current from a to b and are placed in the same magnetic field. Also find the force.

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