Bissoy.com
Doctors Medicines MCQs Q&A

A force \(\vec F\), acting on a electric charge q, in presence of electro-magnetic field, moves the charge parallel to the magnetic field with velocity \(\vec v\). Then \(\vec F\) is equal to (where \(\vec E\)and \(\vec B\) are electric field and magnetic field respectively)

A force \(\vec F\), acting on a electric charge q, in presence of electro-magnetic field, moves the charge parallel to the magnetic field with velocity \(\vec v\). Then \(\vec F\) is equal to (where \(\vec E\)and \(\vec B\) are electric field and magnetic field respectively) Correct Answer <u><span class="math-tex">\(q\vec E\)</span></u>

Concept:

  • The Lorentz force equation describes the magnitude of the force that a moving electric charge would feel as a result of being in the presence of a magnetic field B̅ and an Electric field E̅

i.e.,

  • According to Lorentz’s force when the charge is moving in presence of both an electric and magnetic field, the force acting on it will be the sum of the two forces, i.e.
  • Fnet = F̅elec. + F̅mag. 
  • Fnet = q × E̅ + q (v̅ × B̅)
  • Fnet = q (E̅ + v̅ × B̅)

 

q = charge of the particle

E̅ = Electric field vector

v̅ = velocity vector of the particle

B̅ = magnetic field vector

Explanation:

  • The Force due to the presence of an electric field at due to charge is given by:

F̅elec. = q × E̅ 

  • Also, the force acting on a charged particle moving under the presence of a magnetic field is given by:

F̅mag. = q (v̅ × B̅) = qvBsinθ

  • Where sinθ is the angle between the magnetic field and motion of a charged particle
  • in our case charge particle is moving parallel to the direction of the magnetic field
  • which means that the angle between them (θ) will be zero, hence F̅mag will also be zero.
  • Hence only force due to electric force (F̅elec) will be applied on the charged particle.
  • Thus, in this case, the force exerted on a charge is qE

Related Questions

If the resultant of \(\vec{A}=6\hat{A}\) and \(\vec{B}=8\hat{B}\) is \(\vec{R}=10\hat{R}\) where \(\hat{A},\hat{B}\) and \(\hat{R}\) are the unit vectors along \(\vec{A},\vec{B}\) and \(\vec{R}\), then the value of \(\vec{A}\cdot \vec{B}\) will be
If \(\vec{A},\vec{B}\) and \(\vec{C}\) are coplanar, then the value of \(\vec{A}\cdot \left ( \vec{B} \times \vec{C}\right )\) will be
ABCD is a parallelogram and \(\vec{AC} \) and \(\vec {BD}\) are the diagonals then  \(\vec{AC}+\vec{BD} =?\) 
A circular arc QTS is kept in an external magnetic field $${\overrightarrow {\bf{B}} _0}$$ as shown in figure. The arc carries a current $$l$$. The magnetic field is directed normal and into the page. The force acting on the arc is
Electromagnetic Theory mcq question image
Consider the following three independent cases:
i. Particle A of charge +q moves in free space with a constant velocity $$\overrightarrow {\bf{v}} $$ (v ≪ speed of light).
ii. Particle B of charge +q moves in free space in a circle of radius R with same speed v as In case i.
iii. Particle C having charge -q moves as in case ii.
If the powers radiated by A, B and C are PA, PB and PC respectively then
Two charges q and 2q are placed along the X-axis in front of a grounded, infinite conducting plane, as shown in the figure. They are located respectively at a distance of 0.5 m and 1.5 m from the plane. The force acting on the charge q is
Electromagnetic Theory mcq question image
A snail moves 25 m South, then turns left and moves 125 m, then turns left and moves 10 m, again turns left and moves 75 m and lastly turns right and moves 15 m. Where is the snail now with reference to its starting position?
Deepak moves 5 km south from point R and reaches point P, then moves 7 km right and reaches point Q. Then he takes 2 right turns during which he moves 3 km and 2 km respectively to reach point S. Then he takes left turn and moves 2 km to reach T. Then find the distance between points R and T.
Gaurav cycles towards South-West for a distance of 6 m and stops there. Further, he moves towards East a distance of 10 m and from there he moves towards North-East a distance of 6 m. Next, he moves towards West a distance of 6 m. Now, he moves towards North-West a distance of 2 m. Next, he moves towards West a distance of 4 m and then towards South-West 6 m and stops at that point. Now, where is he from the starting point?
Certain facts about Force are given below. Identify the true information. A. Force is a scalar quantity. B. Gravitational force is the weakest force. C. Electromagnetic force is the strongest force. D. When sum of all forces acting on a body is zero, the body is said to be in a state of equilibrium.