Numerical Problems : Magnetic Effects of Current


Q:1. A framework AKLA forming three sides of a square is made from a copper wire having cross-sectional area 2.5 × 10-6 m2 . The framework can turn about a horizontal axis AA’ , as shown in figure.
The wire is placed in a vertical uniform magnetic field. If on passing a current of 16 amp, through the wire, the framework deflects through an angle θ = 20°, then what is the value of magnetic induction? Given that density of copper = 8.9 gm/c.c.

magnetic field

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Ans: 99 × 10-3 T


Q:2. The magnetic field existing in a region is given by
$ \displaystyle \vec{B} = B_0 (1+ \frac{x}{l})\hat{k}$
A square loop of edge l and carrying a current i , is placed with its edges parallel to the X-Y axes. Find the magnitude of the net magnetic force experienced by the loop.

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Ans: $ \displaystyle i B_0 l \hat{i}$


Q:3. A regular polygon of n sides is formed by bending a wire of total length 2πr which carries a current i
(a) Find the magnetic field B at the centre of the polygon.
(b) By letting n->∞, deduce the expression of the magnetic field at the centre of a circular current.

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Ans: (a) $ \displaystyle \frac{\mu_0 n^2 i}{2\pi^2 r}tan(\frac{\pi}{n}) sin(\frac{\pi}{n}) $
(b) $ \displaystyle \frac{\mu_0 i}{2 r} $


Q:4. A wire loop carrying a current I is placed in the x-y plane as shown in the figure.


(a) If a particle with charge +Q and mass m is placed at the centre P and given a velocity along NP, find its instantaneous acceleration.

(b) If an external uniform magnetic induction field is applied, find the force and the torque acting on the loop due to this field.

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Ans: (a) $ \displaystyle \frac{0.109 \mu_0 I Q v}{ma} $ at an angle 300 to –ve x-axis

(b) $ \displaystyle \frac{0.109 \mu_0 I Q v}{ma} $ , 0.614 a2 I B


Q:5. Two long straight parallel wires are 2 meters apart, perpendicular to the plane of the paper. The wire A carries a current of 9.6 A, directed into the plane of the paper. The wire B carries a current such that the magnetic field of induction at the point P, at a distance of (10/11) m from the wire B, is zero.
Magnetic effect .
Find :
(a) the magnitude and direction of the current in B,

(b) the magnitude of the magnetic field induction at the point S,

(c) the force per unit length on the wire B.

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Ans: (a) 3 A (b)$ \displaystyle \frac{13 \mu_0}{4\pi} $T (c) 2. 88 x 10-6 N/m


Q:6. A very long wire bent at right angle at O. Now current I = 10 A is passed in the wire. Find the magnetic induction at a point P lying on the perpendicular to the wire at O at a distance d = 35 cm.

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Ans: B = 4 × 10-6 T , θ = 45° to the horizontal.


Q:7. In the adjoining diagram, a current-carrying loop pqrs is placed with its sides parallel to a long current-carrying wire. The currents i1 and i2 in the wire and loop are 20 A and 16 A respectively.
If a = 15 cm , b = 6 cm and d = 4 cm , what will be the force on current – loop pqrs ? . What will be the difference in the force , if the current i2 in the loop becomes clockwise instead of anticlockwise ?

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Ans: 1.44 × 10-4 N


Q:8. A current i = 5 amp flows through a thin wire as shown in the figure

(a) Find the magnetic field produced by the current at point ‘ O ‘ in the figure.

(b) If there exists an external magnetic field $ \displaystyle \vec{B} = 14\hat{i} + 14\hat{j}$ T
Calculate the torque acting on the wire.

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Ans: (a) 22.78 μT in the direction $ \hat{k}$ (b)$ \displaystyle \vec{\tau} = 6.7(\hat{j} – \hat{i}) $ T


Q:9. Two long parallel wires carrying currents 2.5 A and I A in the same direction (directed into plane of the paper) are held at P and Q respectively such that they are perpendicular to the plane of paper. The points P and Q are located at distance of 5 meters and 2 meters respectively from a collinear point R.

(a) An electron moving with a velocity of 4 × 105 m/s along the positive x-direction experiences a force of magnitude 3.2 × 10-20 N at the point R. Find the value of I.

(b) Find all the positions at which a third long parallel wire carrying a current of magnitude 2.5 amperes may be placed so that magnetic induction at R is zero

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Ans: (a)4 A (b) x = ± 1 m w.r.t R


Q:10. The diagram shows combination of three cuboidal spaces (1), (2) and (3). Space 1 and 3 contain electric field E as shown while space 2 has magnetic field B. A particle of charge q and mass m is projected as shown with velocity Vocosθ i^+ Vosinθ j^

Find the value of E, so that this particle enters the magnetic field parallel to the x-axis and just passes through point P along the electric field at that point. Find its speed at P. (Neglect the effect of gravity)

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Ans: $ \displaystyle \frac{m V_0^2 sin2\theta}{2 q L} $ ; V0cosθ


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