Consider a magnet surrounded by
Question: Consider a magnet surrounded by a wire with an on/off switch S. If the switch is thrown from the off position (open circuit) to the on position (closed circuit), will a current flow in the circuit? Explain. Solution: No current will be induced as there is no change in any of the magnet or in the area of the circuit. Also, there is no change in the angle....
Read More →A circular coil expands radially in a region of the magnetic
Question: A circular coil expands radially in a region of the magnetic field and no electromotive force is produced in the coil. This can be because (a) the magnetic field is constant. (b) the magnetic field is in the same plane as the circular coil and it may or may not vary. (c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably. (d) there is a constant magnetic field in the perpendicular (to the plane of the coil) direction. Solu...
Read More →The mutual inductance M12 of coil 1 with
Question: The mutual inductance M12 of coil 1 with respect to coil 2 (a) increases when they are brought nearer. (b) depends on the current passing through the coils. (c) increases when one of them is rotated about an axis. (d) is the same as M21 of coil 2 with respect to coil 1. Solution: (a) increases when they are brought nearer. (d) is the same as M21 of coil 2 with respect to coil 1....
Read More →An e.m.f is produced in a coil,
Question: An e.m.f is produced in a coil, which is not connected to an external voltage source. This can be due to (a) the coil is in a time-varying magnetic field. (b) the coil moving in a time-varying magnetic field. (c) the coil moving in a constant magnetic field. (d) the coil is stationary in an external spatially varying magnetic field, which does not change with time. Solution: (a) the coil is in a time-varying magnetic field. (b) the coil moving in a time-varying magnetic field. (c) the ...
Read More →Find the mean deviation about the mean for the following data :
Question: Find the mean deviation about the mean for the following data : Solution: we make the following table from the given data:br data-mce-bogus="1"/ppimg src="https://www.esaral.com/qdb/uploads/2022/02/22/image41790.png" alt="" Therefore, $\overline{\mathrm{x}}=\frac{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}}}=\frac{3100}{50}=62$...
Read More →A metal plate is getting heated.
Question: A metal plate is getting heated. It can be because (a) a direct current is passing through the plate. (b) it is placed in a time-varying magnetic field. (c) it is placed in a space varying magnetic field, but does not vary with time. (d) a current (either direct or alternating) is passing through the plate. Solution: (a) a direct current is passing through the plate. (b) it is placed in a time-varying magnetic field. (c) it is placed in a space varying magnetic field, but does not vary...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x$ Solution: $=\int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x=\int \frac{\sin x-\cos x}{\sqrt{8-(\sin x+\cos x)^{2}+1}} d x$ Let $\sin x+\cos x=t$ $(\cos x-\sin x)=d t$ Therefore, $\int \frac{\sin x-\cos x}{\sqrt{8-(\sin x+\cos x)^{2}+1}} d x=\int \frac{d t}{\sqrt{9-t^{2}}}$ Since we have, $\int \frac{1}{\sqrt{a^{2}-x^{2}}} d x=\sin ^{-1}\left(\frac{x}{a}\right)+c$ $=\int \frac{d t}{\sqrt{9-t^{2}}}=\int...
Read More →The self-inductance L of a solenoid of length
Question: The self-inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as (a) l and A increase. (b) l decreases and A increases. (c) l increases and A decreases. (d) both l and A decrease. Solution: (b) l decreases and A increases....
Read More →Same as problem 4 except the coil A is made
Question: Same as problem 4 except the coil A is made to rotate about a vertical axis. No current flows in B if A is at rest. The current in coil A, when the current in B (at t = 0) is counterclockwise and the coil A is as shown at this instant, t = 0, is (a) constant current clockwise. (b) varying current clockwise. (c) varying current counterclockwise. (d) constant current counterclockwise. Solution: (a) constant current clockwise....
Read More →There are two coils A and B.
Question: There are two coils A and B. A current starts flowing in B as shown, when A is moved towards B and stops when A stops moving. The current in A is counterclockwise. B is kept stationary when A moves. We can infer that (a) there is a constant current in the clockwise direction in A. (b) there is a varying current in A. (c) there is no current in A. (d) there is a constant current in the counterclockwise direction in A. Solution: (d) there is a constant current in the counterclockwise dir...
Read More →Find the mean deviation about the mean for the following data :
Question: Find the mean deviation about the mean for the following data : Solution: we make the following table from the given data:br data-mce-bogus="1"/ppimg src="https://www.esaral.com/qdb/uploads/2022/02/22/image84181.png" alt="" Therefore, $\overline{\mathrm{x}}=\frac{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}}=\frac{12500}{100}=125$...
Read More →A cylindrical bar magnet is rotated about its axis.
Question: A cylindrical bar magnet is rotated about its axis. A wire is connected from the axis and is made to touch the cylindrical surface through a contact. Then (a) a direct current flows in the ammeter A. (b) no current flows through the ammeter A. (c) an alternating sinusoidal current flows through the ammeter A with a time period T=2/. (d) a time-varying non-sinusoidal current flows through the ammeter A. Solution: (b) no current flows through the ammeter A....
Read More →A loop, made of straight edges has six corners at A(0,0,0),
Question: A loop, made of straight edges has six corners at A(0,0,0), B(L,O,0) C(L,L,0), D(0,L,0) E(0,L,L) and F(0,0,L). A magnetic field B = Bo (i + k)T is present in the region. The flux passing through the loop ABCDEFA (in that order) is (a) Bo L2Wb. (b) 2 Bo L2Wb. (c) 2 Bo L2Wb. (d) 4 Bo L2Wb. Solution: (b) 2 Bo L2Wb....
Read More →A square of side L meters lies in the x-y
Question: A square of side L meters lies in the x-y plane in a region, where the magnetic field is given by B = Bo (2i + 3j + 4k) T where Bo is constant. The magnitude of flux passing through the square is (a) 2 Bo L2Wb. (b) 3 Bo L2Wb. (c) 4 Bo L2Wb. (d) 29 B Lo2Wb Solution: (c) 4 Bo L2Wb....
Read More →Find the mean deviation about the mean for the following data :
Question: Find the mean deviation about the mean for the following data : Solution: we make the following table from the given data:br data-mce-bogus="1"/ppimg src="https://www.esaral.com/qdb/uploads/2022/02/22/image37361.png" alt="" Therefore, $\overline{\mathrm{X}}=\frac{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}}=\frac{12500}{100}=125$...
Read More →There are two current-carrying planar coils made each
Question: There are two current-carrying planar coils made each from identical wires of length L. C1 is circular and C2 is square. They are so constructed that they have the same frequency of oscillation when they are placed in the same uniform B and carry the same current. Find a in terms of R. Solution: C1is the circular coil with radius R, length L, and no.of turns per unit length n1 = L/2R C2is the square with side a, perimeter L, and no.of turns per unit length n2 = L/4a Magnetic moment of ...
Read More →Consider the plane S formed by the dipole
Question: Consider the plane S formed by the dipole axis and the axis of the earth. Let P be a point on the magnetic equator and in S. Let Q be the point of intersection of the geographical and magnetic equators. Obtain the declination and dip angle at P and Q. Solution: Point P is in the plane, S is in the north and the declination is zero. The declination is zero for point P as the point lies in the plane S formed by the dipole axis and the axis of the earth The angle of dip is zero for point ...
Read More →Assume the dipole model for earth’s magnetic
Question: Assume the dipole model for earths magnetic field B which is given by Bv = vertical component of magnetic field = 0/4 2m cos /r3, BH = horizontal component of magnetic field = 0/4 2m sin m/r3, = 90o latitude as measured from magnetic equator. Find loci of points for which (i) |B| is minimum (ii) dip angle is zero, and (iii) dip angle is 45o. Solution: (a) |B| is minimum at the magnetic equator. (b) Angle of dip is zero when = /2 (c) When dip angle is 45o = tan-1is the locus....
Read More →What are the dimensions of χ,
Question: What are the dimensions of , the magnetic susceptibility? Consider an H-atom. Guess an expression for , up to a constant by constructing a quantity of dimensions of , out of parameters of the atom: e, m, v, R and 0. Here, m is the electronic mass, v is electronic velocity, R is Bohr radius. Estimate the number so obtained and compare with the value of | | equivalent to 10-5for many solid materials. Solution: m = I/H = intensity of magnetisation/magnetising force is dimensionless as I a...
Read More →Verify the Ampere’s law for the magnetic
Question: Verify the Amperes law for the magnetic field of a point dipole of dipole momentTake 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 the x-z plane. Solution: (a) Along z-axis, magnetic field = 0M/4(1/a2-1/R2) (b) Ma...
Read More →Use (i) the Ampere’s law for H and (ii) continuity of lines of B,
Question: Use (i) the Amperes law for H and (ii) continuity of lines of B, to conclude that inside a bar magnet (a) lines of H run from the N pole to S pole, while (b) lines of B must run from the S pole to N pole. Solution: C is the amperian loop which is given as $\int_{Q}^{P} \vec{H} \cdot \overrightarrow{d l}=\int_{Q}^{P} \frac{\vec{B}}{\mu_{0}} \cdot \overrightarrow{d l}$ Solving the above equation we get the angle between $\vec{H}$ and $\overrightarrow{d l}$ more than $90^{\circ}$ so that ...
Read More →Find the mean deviation about the mean for the following data :
Question: Find the mean deviation about the mean for the following data : Solution: we make the following table from the given data:br data-mce-bogus="1"/ppimg src="https://www.esaral.com/qdb/uploads/2022/02/22/image99856.png" alt="" Therefore, $\overline{\mathrm{X}}=\frac{\sum_{\mathrm{i}=\mathrm{f}}^{6} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}}=\frac{12500}{100}=125$...
Read More →A bar magnet of magnetic moment m and moment
Question: A bar magnet of magnetic moment m and moment of inertia I is cut into two equal pieces, perpendicular to length. Let T be the period of oscillations of the original magnet about an axis through the midpoint, perpendicular to the length, in a magnetic field B. What would be the similar period T for each piece? Solution: T is the time period I is the moment of inertia m is the mass of the magnet B is the magnetic field T = 2I/MB Magnetic dipole moment M = M/2 Time period is given as T = ...
Read More →Suppose we want to verify the analogy between
Question: 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 movements are verified to be identical. Solution: pE sin = B sin pE = B E = cB pcB = B p = /c...
Read More →Three identical bar magnets are riveted together
Question: Three identical bar magnets are riveted together at the centre in the same plane as shown in the figure. This system is placed at rest in a slowly varying magnetic field. It is found that the system of magnets does not show any motion. The north-south poles of one magnet is shown in the figure. Determine the poles of the remaining two. Solution: The system will have a net torque and the net force equal to zero as the system is in equilibrium....
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