Q7) Derive an expression for the magnitude of the magnetic field at point P in the diagram below. Is it into or out of the page? Figure not drawn to scale.

A proton enters a region with a uniform electric field E=5.0kV/m and a uniform magnetic field B=5.0104kT. The proton has initial velocity v0=2.5105m/s. How far along the z axis does the proton travel after it undergoes three complete revolutions?

The right-hand rule is a way to determine the direction of the magnetic field produced by moving charges. Imagine wrapping your right hand around the path of the charges so that the positive charges (or the current) flow from the little finger side of your fist to the thumb side (Figure 8.53). Then your fingers circle the path in the same direction as the magnetic field lines. Use this rule to verify the directions of the magnetic fields shown in Figures 8.8 and 8.10. How would you use the rule to find the direction of the magnetic field lines around a moving negative charge?

Neurons in our bodies carry weak currents that produce detectable magnetic fields. A technique called magnetoencephalography, or MEG, is used to study electrical activity in the brain using this concept This technique is capable of detecting magnetic fields as weak as 1.0 1015 T. Model the neuron as a long wire carrying a current and find the current it must carry to produce a field of this magnitude at a distance of 4.0 cm from the neuron.

A current I flows around a wire bent into the shape of a square of side a. What is tire magnetic field at the point P that is a distance z above the center of the square (see the accompanying figure)?

Consider a magnetic field that is uniform in direction throughout a certain volume. (a) Can the field be uniform in magnitude? (b) Must it be uniform in magnitude? Give evidence for your answers.

(a) A physicist performing a sensitive measurement wants to limit the magnetic force on a moving charge in her equipment to less than 1.001012N. What is the greatest the charge can be if it moves at a maximum speed of 30.0 m/s in the Earth’s field? (b) Discuss whether it would be difficult to limit the charge to less than the value found in (a) by competing it with typical static electricity and noting that static is often absent.

A laboratory electromagnet produces a magnetic field of magnitude 1.50 T. A proton moves through this field with a speed of 6.00 106 m/s. (a) Find the magnitude of the maximum magnetic force that could he exerted on the proton. (b) What is the magnitude of the maximum acceleration of the proton? (c) Would the field exert the same magnetic force on an electron moving through the field with the same speed? (d) Would the electron experience the same acceleration? Explain.

A laboratory electromagnet produces a magnetic field of magnitude 1.50 T. A proton moves through this field with a speed of 6.00 106 m/s. (a) Find the magnitude of the maximum magnetic force that could be exerted on the proton. (b) What is the magnitude of the maximum acceleration of the proton? (c) Would the field exert the same magnetic force on an electron moving through the field with the same speed? (d) Would the electron undergo the same acceleration? Explain.

(a) A DC power line for a light-rail system carries 1000 A at an angle of 30.0° to the Earth’s 5.00105-T field. What is the force on a 100-m section of this line? (b) Discuss practical concerns this presents, if any.