CBSE Class 12 · 2012 · Delhi · Magnetic Effects of CurrentShort Answer

Two identical circular wires P and Q, each of radius

R

and carrying current

I

, are kept in perpendicular planes such that they have a common centre. Find the magnitude and direction of the net magnetic field at the common centre of the two coils.

Answer: $B = \frac{μ _{0} I}{2 R}$ , directed at $4 5^{\circ}$ to the plane of each coil.

Solution

Each coil produces a field at the centre of magnitude

B_{0} = \frac{μ _{0} I}{2 R}

, one directed along the axis of P and the other along the axis of Q. As the planes are perpendicular, these two fields are mutually perpendicular, so

B = B_{0}^{2} + B_{0}^{2} = 2 B_{0} = 2 \cdot \frac{μ _{0} I}{2 R} = \frac{μ _{0} I}{2 R} .

The resultant makes an angle of

4 5^{\circ}

with the plane of each coil.

CBSE Class 12 Board · 2012 · Delhi · Subjective

Practise more: all CBSE board PYQs on Magnetic Effects of Current →

More board questions on Magnetic Effects of Current

(i) State and explain Ampere's circuital law.
(ii) Two long straight parallel wires separated by $20 cm$ carry $5 A$ and $10 A$ current respectively in the same direction. Find the magnitude and direction of the net magnetic field at a point midway between …
CBSE 2024View solution →
Assertion (A): The energy of a charged particle moving in a magnetic field does not change.
Reason (R): It is because the work done by the magnetic force on the charge moving in a magnetic field is zero.
CBSE 2024View solution →
Derive an expression for the magnetic force $F$ acting on a straight conductor of length $L$ carrying current $I$ in an external magnetic field $B$ . Is it valid when the conductor is in zig-zag form? Justify.
CBSE 2024View solution →
An electron moving with a velocity $v = (1.0 \times 1 0^{7} m/s) \hat{i} + (0.5 \times 1 0^{7} m/s) \hat{j}$ enters a region of uniform magnetic field $B = (0.5 mT) \hat{j}$ . Find the radius of the circular path described by it. While rotating, does …
CBSE 2024View solution →
Beams of electrons and protons move parallel to each other in the same direction. They
CBSE 2023View solution →
A long straight wire of radius $a$ carries a steady current $I$ distributed uniformly across its cross-section. The ratio of the magnitudes of the magnetic field $B_{1}$ at $\frac{a}{2}$ and $B_{2}$ at a distance $2 a$ from the axis is
CBSE 2023View solution →