(C) The magnetic field at the centre of the cube due to a square loop $A B C D$ is given as $B$. The path $D A E F G C D$ can be analyzed as a superpo

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(C) The magnetic field at the centre of the cube due to a square loop $A B C D$ is given as $B$. The path $D A E F G C D$ can be analyzed as a superposition of three square loops oriented in the $xy$,$yz$,and $zx$ planes. By applying the principle of superposition,the net magnetic field at the centre is the vector sum of the magnetic fields produced by these three loops. Let the magnetic field vectors be represented as $\vec{B}_1 = B \hat{i}$,$\vec{B}_2 = B \hat{j}$,and $\vec{B}_3 = -B \hat{k}$. The net magnetic field is $\vec{B}_{net} = B \hat{i} + B \hat{j} - B \hat{k}$. The magnitude of the resultant magnetic field is $|\vec{B}_{net}| = \sqrt{B^2 + B^2 + (-B)^2} = \sqrt{3B^2} = \sqrt{3} B$.

Class 12 Physics Moving Charges and Magnetism Mix Examples-Moving Charges and Magnetism

The current flowing along the path $A B C D$ of a cube (shown in the left figure) produces a magnetic field at the centre of the cube of magnitude $B$. Dashed lines depict the non-conducting part of the cube. Consider a cubical shape shown to the right which is identical in size and shape to the left. If the same current now flows in along the path $D A E F G C D$,then the magnitude of the magnetic field at the centre will be

KVPY 2018 All KVPY

A
zero
B
$\sqrt{2} B$
C
$\sqrt{3} B$
D
$B$

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Class 12 Questions

Class 12

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Moving Charges and Magnetism

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Mix Examples-Moving Charges and Magnetism

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The dimensional formula of $\frac{1}{2} \mu_0 H^2$ (where $\mu_0$ is the permeability of free space and $H$ is the magnetic field intensity) is:

MediumTS EAMCET 2011

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Match the following and find the correct pairs.
List-$I$ List-$II$
$(A)$ Fleming's left hand rule $(i)$ Direction of induced current
$(B)$ Right hand thumb rule (ii) Magnitude and direction of magnetic induction
$(C)$ Biot-Savart law (iii) Direction of force due to magnetic induction
$(D)$ Fleming's right hand rule (iv) Direction of magnetic lines due to current

List-$I$	List-$II$
$(A)$ Fleming's left hand rule	$(i)$ Direction of induced current
$(B)$ Right hand thumb rule	(ii) Magnitude and direction of magnetic induction
$(C)$ Biot-Savart law	(iii) Direction of force due to magnetic induction
$(D)$ Fleming's right hand rule	(iv) Direction of magnetic lines due to current

EasyAP EAMCET 2011

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Two circular coils $X$ and $Y$,having an equal number of turns,carry equal currents in the same sense and subtend the same solid angle at point $O$. If the smaller coil $X$ is midway between $O$ and $Y$,then if we represent the magnetic induction due to the bigger coil $Y$ at $O$ as $B_Y$ and that due to the smaller coil $X$ at $O$ as $B_X$,then:

Difficult

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When a proton is released from rest in a room,it starts with an initial acceleration $a_0$ towards west. When it is projected towards north with a speed $v_0$,it moves with an initial acceleration $3a_0$ towards west. The electric and magnetic fields in the room are

MediumAIPMT 2013

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Two long current-carrying thin wires,both with current $I$,are held by insulating threads of length $L$ and are in equilibrium as shown in the figure,with threads making an angle $\theta$ with the vertical. If the wires have mass $\lambda$ per unit length,then the value of current $I$ is ($g =$ gravitational acceleration).

DifficultJEE MAIN 2015

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The dimensional formula of $\frac{1}{2} \mu_0 H^2$ (where $\mu_0$ is the permeability of free space and $H$ is the magnetic field intensity) is:

When a proton is released from rest in a room,it starts with an initial acceleration $a_0$ towards west. When it is projected towards north with a speed $v_0$,it moves with an initial acceleration $3a_0$ towards west. The electric and magnetic fields in the room are

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