Question

in out ˇ B θ θ →B →B →B →B →B

(a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields in the figure, as shown.
(b) Repeat part (a), assuming the moving particle is an electron.

Field		Force Direction	a				b				c				d				e				f				Field		Force Direction	a				b				c				d				e				f

Answer 1

Concepts and reason

The concepts required to solve the given problem is magnetic force on a charge moving in a magnetic field and cross product.

Determine the direction of force on proton in each given figure by using expression for magnetic force and by using velocity and magnetic field vectors. Then, take the opposite directions as the force on the proton to obtain the direction of force on the electron.

Fundamentals

The magnetic force on a charge moving in a magnetic field with velocity is given by following expression.

Here, q is the charge.

The cross product between two-unit vectors in same direction is equal to zero.

Other properties of cross product are given as follows:

(a)

The magnetic force on a charge moving in a magnetic field with velocity is given by following expression.

Substitute for and for in the above equation.

The magnetic force on a charge moving in a magnetic field with velocity is given by following expression.

Substitute for and for in the above equation.

The magnetic force on a charge moving in a magnetic field with velocity is given by following expression.

Substitute for and for in the above equation.

The magnetic force on a charge moving in a magnetic field with velocity is given by following expression.

Substitute for and for in the above equation.

The magnetic force on a charge moving in a magnetic field with velocity is given by following expression.

Substitute for and for in the above equation.

The magnetic force on a charge moving in a magnetic field with velocity is given by following expression.

Substitute for and for in the above equation.

(b)

The direction of force on electron in figure (a) is to the right.

The direction of force on electron in figure (b) is out of the page.

The direction of force on electron in figure (c) is into the page.

The direction of force on electron in figure (d) is downward.

The direction of force on electron in figure (e) is out of the page.

The direction of force on electron in figure (f) is into the page.

Ans: Part a.a

The direction of force on the proton in figure (a) is to the left.

Part a.b

The direction of force on the proton in figure (b) is into the page.

Part a.c

The direction of force on the proton in figure (c) is out of the page.

Part a.d

The direction of force on the proton in figure (d) is upward.

Part a.e

The direction of force on the proton in figure (e) is into the page.

Part a.f

The direction of force on the proton in figure (f) is out of the page.

Part b.a

The direction of force on electron in figure (a) is to the right.

Part b.b

The direction of force on electron in figure (b) is out of the page.

Part b.c

The direction of force on electron in figure (c) is into the page.

Part b.d

The direction of force on electron in figure (d) is downward.

Part b.e

The direction of force on electron in figure (e) is out of the page.

Part b.f

The direction of force on electron in figure (f) is into the page.