Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Class 12 Physics 35 Years JEE Mains &Advance Past year Paper

Created by: Abhishek Kapoor

JEE : Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

The document Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev is a part of the JEE Course Class 12 Physics 35 Years JEE Mains &Advance Past year Paper.
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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 Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev 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

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

In ΔPRM,

16x2 = PM2 + (5x – a)2 … (iii)

⇒ 7 x2 = 25 x2- 10xa ⇒  10xa =  18x2

 a = 1.8 x … (iv)

From (ii) & (iv),

9 x2 = PM2+ (1.8x)2

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev
Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

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

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Comparing it with B =Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

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 = I0cos(300 t) where I0 is constant. If the magnetic moment of the loop is Nμ0I0sin (300 t), then ‘N’ is

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Ans. 6

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

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev (current passing through the loop)

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

The magnetic moment of the loop = (current in the loop) × πr2

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Comparing it with the expression given in the question we get

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

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 Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev then the value of N is
Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Ans.5

Solution. Current density J =Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

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

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

The magnetic field at P due to the current (I’) flowing in opposite direction is

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

∴ The net magnetic field is

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Q.4. Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed u between the wires in the same plane at a distance X1 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 R1. In contrast, if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R2. If Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev  the value ofInteger Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev   is

Ans. 3

Solution. Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

Integer Value of Moving Charges and Magnetism the Following, of Moving Charges and Magnetism , JEE Notes | EduRev

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