Question

Let the current $i=2A$ be flowing in each part of a wire frame as shown in the figure. The frame is a combination of two equilateral triangles ACD and CDE of side 1 m. It is placed in uniform magnetic field B = 4 T acting perpendicular to the plane of frame. The magnitude of magnetic forces acting on the frame is:
(A) 24 N
(B) Zero
(C) 16 N
(D) 8 N

Answer 1

Hint: We know that a magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetized materials. A charge that is moving in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. The magnetic field is generated by electric currents due to the motion of convection currents of a mixture of molten iron and nickel in the Earth's outer core: these convection currents are caused by heat escaping from the core, a natural process called a geodynamo.

Complete step by step answer
We know that the net force is the vector sum of all the forces acting on an object. When an object is in equilibrium (either at rest or moving with constant velocity), the net force acting on it is zero. A vector can only have zero magnitude if all of its components are zero. The action from a force can cause an object to move or speed up (accelerate), to slow down (decelerate), to stop, or to change direction. Since any change in velocity is considered acceleration, it can be said that a force on an object results in the acceleration of an object.
When two or more forces act on an object, the resultant force can be found by adding up the individual forces. A resultant force is the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body. The defining feature of a resultant force, or resultant force-torque, is that it has the same effect on the rigid body as the original system of forces.
According to Newton's First Law of motion, an object remains in the same state of motion unless a resultant force acts on it. If the resultant force on an object is zero, this means: a stationary object stays stationary. a moving object continues to move at the same velocity.
$\overrightarrow{\mathrm{F}}_{\mathrm{CAD}}=\overrightarrow{\mathrm{F}}_{\mathrm{CED}}=\overrightarrow{\mathrm{F}}_{\mathrm{CD}}$
Net force on the frame:
$\therefore \overrightarrow{\mathrm{F}}_{\mathrm{net}}=3 \times \overrightarrow{\mathrm{F}}_{\mathrm{CD}}$
$=3 \times(2 \times 1 \times 4)=24 \mathrm{N}$

So, option A is correct.

Note: We can conclude that the resultant is the vector sum of all the individual vectors. The resultant is the result of combining the individual vectors together. The resultant can be determined by adding the individual forces together using vector addition methods. Net force, also known as resultant force, is a vector quantity produced when two or more forces act upon one object. The concept of net force is the same as the mathematical concept of vector addition. When two forces acting on an object are equal in size but act in opposite directions, we say that they are balanced forces. A stationary object stays still. A moving object continues to move at the same speed and in the same direction.