HC Verma solutions for Concepts of Physics Vol. 2 [English] Class 11 and 12 chapter 13 - Magnetic Field due to a Current [Latest edition]

An electric current flows in a wire from north to south. What will be the direction of the magnetic field due to this wire at a point (a) east of the wire, (b) west of the wire, (c) vertically above the wire and (d) vertically below the wire? 

In Ampere's  \[\oint \vec{B}  \cdot d \vec{l}  =  \mu_0 i,\] the current outside the curve is not included on the right hand side. Does it mean  that the magnetic field B calculated by using Ampere's law, gives the contribution of only the currents crossing the area bounded by the curve?  

A vertical wire carries a current in upward direction. An electron beam sent horizontally towards the wire will be deflected

A current-carrying, straight wire is kept along the axis of a circular loop carrying a current. This straight wire

A proton beam is going from north to south and an electron beam is going from south to north. Neglecting the earth's magnetic field, the electron beam will be deflected

A circular loop is kept in that vertical plane which contains the north-south direction. It carries a current that is towards north at the topmost point. Let A be a point on the axis of the circle to the east of it and B a point on this axis to the west of it. The magnetic field due to the loop 

Consider the situation shown in figure. The straight wire is fixed but the loop can move under magnetic force. The loop will

A charged particle is moved along a magnetic field line. The magnetic force on the particle is 

A moving charge produces

A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to

Two particles X and Y having equal charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii R₁ and R₂ respectively. The ratio of the mass of X to that of Y is ______.

Two parallel wires carry currents of 20 A and 40 A in opposite directions. Another wire carying a current anti parallel to 20 A is placed midway between the two wires. T he magnetic force on it will be

Two parallel, long wires carry currents i₁ and i₂ with i₁ > i₂. When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 µT. If the direction of i₂ is reversed, the field becomes 30 µT. The ratio i₁/i₂ is 

Consider a long, straight wire of cross-sectional area A carrying a current i. Let there be n free electrons per unit volume. An observer places himself on a trolley moving in the direction opposite to the current with a speed  \[v = \frac{i}{\text{nAe}}\] and separation from the wire by a distance r. The magnetic field seen by the observer is very nearly  

The magnetic field at the origin due to a current element  \[i d \vec{l}\] placed at a position \[\vec{r}\] is 

(a)\[\frac{\mu_0 i}{4\pi}\frac{d \vec{l} \times \vec{r}}{r^3}\]

(b) \[- \frac{\mu_0 i}{4\pi}\frac{\vec{r} \times d \vec{l}}{r^3}\]

(c) \[\frac{\mu_0 i}{4\pi}\frac{\vec{r} \times d \vec{l}}{r^3}\]

(d) \[- \frac{\mu_0 i}{4\pi}\frac{d \vec{l} \times \vec{r}}{r^3}\] 

Consider three quantities  \[x = E/B,   y = \sqrt{1/ \mu_0 \epsilon_0}\] and \[z = \frac{l}{CR}\] . Here, l is the length of a wire, C is a capacitance and R is a resistance. All other symbols have standard meanings.

(a) x, y have the same dimensions.
(b) y, z have the same dimensions.
(c) z, x have the same dimensions.
(d) None of the three pairs have the same dimensions.

A long, straight wire carries a current along the z-axis, One can find two points in the x−y plane such that
(a) the magnetic fields are equal
(b) the directions of the magnetic fields are the same
(c) the magnitudes of the magnetic fields are equal
(d) the field at one point is opposite to that at the other point.

A long, straight wire of radius R carries a current distributed uniformly over its cross section. T he magnitude of the magnetic field is
(a) maximum at the axis of the wire
(b) minimum at the axis of the wire
(c) maximum at the surface of the wire
(d) minimum at the surface of the wire.

A hollow tube is carrying an electric current along its length distributed uniformly over its surface. The magnetic field
(a) increases linearly from the axis to the surface
(b) is constant inside the tube
(c) is zero at the axis
(d) is zero just outside the tube.

In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero
(a) outside the cable
(b) inside the inner conductor
(c) inside the outer conductor
(d) in between the tow conductors.

A steady electric current is flowing through a cylindrical conductor.
(a) The electric field at the axis of the conductor is zero.
(b) The magnetic field at the axis of the conductor is zero.
(c) The electric field in the vicinity of the conductor is zero.
(d) The magnetic field in the vicinity of the conductor is zero.

Using the formula \[\vec{F} = q \vec{v} \times \vec{B} \text{ and } B = \frac{\mu_0 i}{2\pi r}\]show that the SI units of the magnetic field B and the permeability constant µ₀ may be written as N mA⁻¹ and NA⁻² respectively.

A current of 10 A is established in a long wire along the positive z-axis. Find the magnetic field  \[\vec{B}\]  at the point (1 m, 0, 0).

A copper wire of diameter 1.6 mm carries a current of 20 A. Find the maximum magnitude of the magnetic field `vecB` due to this current.

A long, straight wire carrying a current of 1.0 A is placed horizontally in a uniform magnetic field B = 1.0 × 10⁻⁵ T pointing vertically upward figure. Find the magnitude of the resultant magnetic field at the points P and Q, both situated at a distance of 2.0 cm from the wire in the same horizontal plane. 

A long, straight wire of radius r carries a current i and is placed horizontally in a uniform magnetic field B pointing vertically upward. The current is uniformly distributed over its cross section. (a) At what points will the resultant magnetic field have maximum magnitude? What will be the maximum magnitude? (b) What will be the minimum  magnitude of the resultant magnetic field?

A long, straight wire carrying a current of 30 A is placed in an external, uniform magnetic field of 4.0 × 10⁻⁴ T parallel to the current. Find the magnitude of the resultant magnetic field at a point 2.0 cm away from the wire.

A long, vertical wire carrying a current of 10 A in the upward direction is placed in a region where a horizontal magnetic field of magnitude 2.0 × 10⁻³ T exists from south to north. Find the point where the resultant magnetic field is zero. 

Figure shows two parallel wires separated by a distance of 4.0 cm and carrying equal currents of 10 A along opposite directions. Find the magnitude of the magnetic field B at the points A₁, A₂, A₃. 

Two parallel wires carry equal currents of 10 A along the same direction and are separated by a distance of 2.0 cm. Find the magnetic field at a point which is 2.0 cm away from each of these wires.

Two long, straight wires, each carrying a current of 5 A, are placed along the x- and y-axis respectively. The currents point along the positive directions of the axes. Find the magnetic fields at the points (a) (1 m, 1 m), (b) (−1 m, 1 m), (c) (−1 m, −1 m) and (d) (1 m, −1 m). 

Four long, straight wires, each carrying a current of 5.0 A, are placed in a plane as shown in figure. The points of intersection form a square of side 5.0 cm.
(a) Find the magnetic field at the centre P of the square.
(b) Q₁, Q₂, Q₃, and Q₄, are points situated on the diagonals of the square and at a distance from P that is equal to the diagonal of the square. Find the magnetic fields at these points. 

Figure shows a long wire bent at the middle to form a right angle. Show that the magnitudes of the magnetic fields at the point P, Q, R and S are equal and find this magnitude. 

Consider a straight piece of length x of a wire carrying a current i. Let P be a point on the perpendicular bisector of the piece, situated at a distance d from its middle point. Show that for d >> x, the magnetic field at P varies as 1/d² whereas for d << x, it varies as 1/d.  

A long, straight wire carries a current i. Let B₁ be the magnetic field at a point P at a distance d from the wire. Consider a section of length l of this wire such that the point P lies on a perpendicular bisector of the section B₂ be the magnetic field at this point due to this second only. Find the value of d/l so that B₂ differs from B₁ by 1%.    

Figure shows a square loop ABCD with edge-length a. The resistance of the wire ABC is r and that of ADC is 2r. Find the magnetic field B at the centre of the loop assuming uniform wires. 

Figure shows a square loop of edge a made of a uniform wire. A current i enters the loop at the point A and leaves it at the point C. Find the magnetic field at the point P which is on the perpendicular bisector of AB at a distance a/4 from it. 

Consider the situation described in the previous problem. Suppose the current i enters the loop at the points A and leaves it at the point B. Find the magnetic field at the centre of the loop. 

The wire ABC shown in figure forms an equilateral triangle. Find the magnetic field B at the centre O of the triangle assuming the wire to be uniform. 

A wire of length l is bent in the form of an equilateral triangle and carries an electric current i. (a) Find the magnetic field B at the centre. (b) If the wire is bent in the form of a square, what would be the value of B at the centre?

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 filed B at the centre of the polygon. (b) By letting n → ∞, deduce the expression for the magnetic field at the centre of a circular current. 

Each of the batteries shown in figure has an emf equal to 5 V. Show that the magnetic field B at the point P  is zero for any set of values of the resistances. 

Two parallel wires separated by a distance of 10 cm carry currents of 10 A and 40 A along the same direction. Where should a third current by placed so that it experiences no magnetic force?

Figure shows a part of an electric circuit. The wires AB, CD and EF are long and have identical resistance. The  separation between the neighbouring wires is 1.0 cm. The wires AE and BF have negligible resistance and the ammeter reads 30 A. Calculate the magnetic force per unit length of AB and CD. 

A long, straight wire is fixed horizontally and carries a current of 50.0 A. A second wire having linear mass density 1.0 × 10⁻⁴ kg m⁻¹ is placed parallel to and directly above this wire at a separation of 5.0 mm. What current should this second wire carry such that the magnetic repulsion can balance its weight? 

A square loop PQRS carrying a current of 6.0 A is placed near a long wire carrying 10 A as shown in figure. (a) Show that the magnetic force acting on the part PQ is equal and opposite to the part RS. (b) Find the magnetic force on the square loop. 

A conducting circular loop of radius a is connected to two long, straight wires. The straight wires carry a current i as shown in figure. Find the magnetic field B at the centre of the loop. 

Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centres coincide. Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense. 

Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centres coincide. If the outer coil is rotated through 90° about a diameter, Find the  magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.

A circular loop of radius R carries a current I. Another circular loop of radius r(<<R) carries a current i and is placed at the centre of the larger loop. The planes of the two circles are at right angle to each other. Find the torque acting on the smaller loop. 

A circular loop of radius r carrying a current i is held at the centre of another circular loop of radius R(>>r) carrying a current I. The plane of the smaller loop makes an angle of 30° with that of the larger loop. If the smaller loop is held fixed in this position by applying a single force at a point on its periphery, what would be the minimum magnitude of this force? 

A circular coil of 200 turns has a radius of 10 cm and carries a current of 2.0 A. (a) Find the magnitude of the magnetic field \[\vec{B}\] at the centre of the coil. (b) At what distance from the centre along the axis of the coil will the field B drop to half its value at the centre?

A long, cylindrical wire of radius b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnetic field at a point inside the wire at a distance a from the axis.  

Sometimes we show an idealised magnetic field which is uniform in a given region and falls to zero abruptly. One such field is represented in figure. Using Ampere's law over the path PQRS, show that such a field is not possible. 

Two large metal sheets carry currents as shown in figure. The current through a strip of width dl is Kdl where K is a constant. Find the magnetic field at the points P, Q and R.

A tightly-wound solenoid of radius a and length l has n turns per unit length. It carries an electric current i. Consider a length dx of the solenoid at a distance x from one end. This contains n dx turns and may be approximated as a circular current i n dx. (a) Write the magnetic field at the centre of the solenoid due to this circular current. Integrate this expression under proper limits to find the magnetic field at the centre of the solenoid. (b) verify that if l >> a, the field tends to B = µ₀ni and if a >> l, the field tends to `B =(mu_0nil)/(2a)` . Interpret these results.