Advertisements
Advertisements
Question
There are two current carrying planar coils made each from identical wires of length L. C1 is circular (radius R) and C2 is square (side a). They are so constructed that they have same frequency of oscillation when they are placed in the same uniform B and carry the same current. Find a in terms of R.
Advertisements
Solution
As the frequencies (ω) for both coil are given same
ω1 = ω2
`(2pi)/T_1 = (2pi)/T`
So the time period of both the coil C1 and C2 are equal so T1 = T2
`2pi sqrt(I_1/(m_1B)) = 2pi sqrt(I_2/(m_2B))`
`sqrt(I_1/m_1) = sqrt(I_2/m_2)`
As B is same in both coils so squaring both side we get,
`I_1/I_2 = m_1/m_2` ......(I)
I1, I2 are the moment of inertia of coils C1 and C2 placed in same magnetic field B.
`I_1 = (mR^2)/2` ......(II)
`I_2 = (ma^2)/12` ......(III)
As the length of wire is same and identical so masses m1 = m2 = m
For circular-shaped coil magnetic moment
m1 = n1IA1 ......[∵ Current (i) in both are same, i.e. I1 = I2 = I]
`m_1 = L/(2piR) * I * piR^2` ......[∵ L = 2πRn1]
`m_1 = (LIR)/2` .......(IV)
For square-shaped coil, magnetic moment
`m_2 = n_2IA_2` as current I1 = I2 = I ...(Given) = `L/(4a) I.a^2`
`m_2 = (LIa)/4`
Substitute II, III, IV, V in I
⇒ R22 × 12a2 = R2 × 4a
⇒ Ra = 13
⇒ 3R = a
APPEARS IN
RELATED QUESTIONS
Magnetic lines of force are closed continuous curves.
How are the magnetic field lines different from the electrostatic field lines?
Answer the following question.
Write the four important properties of the magnetic field lines due to a bar magnet.
Answer the following question in brief.
What happens if a bar magnet is cut into two pieces transverse to its length/along its length?
Solve the following problem.
A magnetic pole of a bar magnet with a pole strength of 100 A m is 20 cm away from the centre of a bar magnet. The bar magnet has a pole strength of 200 A m and has a length of 5 cm. If the magnetic pole is on the axis of the bar magnet, find the force on the magnetic pole.
If the bar magnet is turned around by 180°, where will the new null points be located?
According to the dipole analogy 1/ε0 corresponds to ______.
Magnetic moment for solenoid and corresponding bar magnet is ______.
When current is double deflection is also doubled in
A magnetic needle suspended freely orients itself:-
A toroid of n turns, mean radius R and cross-sectional radius a carries current I. It is placed on a horizontal table taken as x-y plane. Its magnetic moment m ______.
A proton has spin and magnetic moment just like an electron. Why then its effect is neglected in magnetism of materials?
A ball of superconducting material is dipped in liquid nitrogen and placed near a bar magnet. (i) In which direction will it move? (ii) What will be the direction of it’s magnetic moment?
Suppose we want to verify the analogy between electrostatic and magnetostatic by an explicit experiment. Consider the motion of (i) electric dipole p in an electrostatic field E and (ii) magnetic dipole m in a magnetic field B. Write down a set of conditions on E, B, p, m so that the two motions are verified to be identical. (Assume identical initial conditions.)
Verify the Ampere’s law for magnetic field of a point dipole of dipole moment m = m`hatk`. Take C as the closed curve running clockwise along (i) the z-axis from z = a > 0 to z = R; (ii) along the quarter circle of radius R and centre at the origin, in the first quadrant of x-z plane; (iii) along the x-axis from x = R to x = a, and (iv) along the quarter circle of radius a and centre at the origin in the first quadrant of x-z plane.
A long straight wire of circular cross section of radius 'a' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of magnitudes of the magnetic field at a point `a/2` above the surface of wire to that of a point `a/2` below its surface is ______.
