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**Q.1. A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x, PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is find the value of k.**

**Ans. **7

**Solution. **

The right angled triangle is shown in the figure. Let us drop a perpendicular from P on QR which cuts QR at M.

The magnatic field due to currents in PQ and RP at P is zero.

The magnetic field due to current in QR at P is

In Î”PRM,

16x^{2} = PM^{2} + (5x â€“ a)^{2} â€¦ (iii)

â‡’ 7 x^{2} = 25 x^{2}- 10xa â‡’ 10xa = 18x^{2}

â‡’ ^{ }a = 1.8 x â€¦ (iv)

From (ii) & (iv),

9 x^{2} = PM^{2}+ (1.8x)^{2}

From (i), (v), (vi) and (vii),

Comparing it with B =

**Q.2. A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as I = I _{0}cos(300 t) where I_{0} is constant. If the magnetic moment of the loop is NÎ¼_{0}I_{0}sin (300 t), then â€˜Nâ€™ is**

**Ans. **6

**Solution. **Let us consider an amperian loop ABCD which is a rectangle as shown in the figure. Applying ampereâ€™s circuital law we get

(current passing through the loop)

The magnetic moment of the loop = (current in the loop) Ã— Ï€r^{2}

^{}

^{}

^{}

Comparing it with the expression given in the question we get

**Q.3.A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinity long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given by then the value of N is**

**Ans.**5

**Solution. **Current density J =

Let us consider the cavity to have current I' flowing in both the directions.

The magnetic field at P due to the current flowing through the cylinder

The magnetic field at P due to the current (Iâ€™) flowing in opposite direction is

âˆ´ The net magnetic field is

**Q.4. Two parallel wires in the plane of the paper are distance X _{0} apart. A point charge is moving with speed u between the wires in the same plane at a distance X_{1} from one of the wires. When the wires carry current of magnitude I in the same direction, the radius of curvature of the path of the point charge is R_{1}. In contrast, if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R_{2}. If the value of is**

**Ans. **3

**Solution. **

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