Explanation 1) Concept: We can use the formula of magnetic force to determine the force on the charges with different directions of velocities. Then from that, we can find the electric field. Then using the relation between the electric field and voltage, we can find the voltage across the solids corresponding to different directions velocities. Using this, we can rank the choices for directions of velocity according to the magnitude of the voltage across the solids. 2) Formulae: i) F → = q v → × B → = q v B s i n θ ii) E = F B q iii) V = E d 3) Given: Magnetic field B is along x direction, and we are given six different choices of velocities. Dimensions of rectangular boxes are given in the figure. 4) Calculations: a) Ranking of choices according to potential differences developed: In the given figure, uniform magnetic field ( B ) is along positive x direction, and velocity of rectangular solid ( v ) is also along + x direction. The angle between these two vectors is zero, and the acting on the charges will be zero. Hence potential difference could not be developed for this choice of velocity. F → B = q v → × B → = q v B s i n θ F → = q v B s i n 0 F → = 0 E = F B q = 0 V = E d = 0 Similarly, velocity of rectangular solid ( v ) along - x direction will cause no force on charges, and the force acting on the charges is zero. Here, the angle between magnetic field ( B ) and velocity ( V ) is 180 ° . V = 0 When the velocity is along + y direction and magnetic field ( B ) along + x direction, the force will act on the charge particles because velocity and magnetic field are perpendicular to each other, and we get a non-zero force. F → B = - e v y ^ × B x ^ = e v B ( z ^ ) E = F B q = 2 e v B e = v B V = E d = d v B The force will act on negative charges along + z direction

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.

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Chapter 28, Problem 3Q

To determine

To rank:

a) The six choices of velocity according to the potential difference developed across the solid.

b) For which choice will the front face be at a lower potential?

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Chapter 28, Problem 2Q

Chapter 28, Problem 4Q

Chapter 28 Solutions

Fundamentals of Physics Extended

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To rank: a) The six choices of velocity according to the potential difference developed across the solid. b) For which choice will the front face be at a lower potential?

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To rank: a) The six choices of velocity according to the potential difference developed across the solid. b) For which choice will the front face be at a lower potential?

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Chapter 28 Solutions

To rank:

a) The six choices of velocity according to the potential difference developed across the solid.

b) For which choice will the front face be at a lower potential?