Midterm 2, Physics 6B Summer UCLA

# Midterm 2, Physics 6B Summer UCLA - Problem 1(a v vo f"= f...

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Problem 1 (a) " f = f v ± v o v m v s # \$ % & ( 1500 Hz = f v + v o v # \$ % & ( 1000 Hz = f v ) v o v # \$ % & ( 1500 Hz 1000 Hz = 3 2 = v + v o v ) v o 3 v ) v o ( ) = 2 v + v o ( ) 5 v o = v v o = 1 5 v = 1 5 # \$ % & ( 343 m s ( ) = 68.6 m s (b) f = 1500 Hz v v + v o " # \$ % & = 1500 Hz 343 m s 343 m s + 68.6 m s " # \$ % & = 1250 Hz or: f = 1000 Hz v v " v o # \$ % & ( = 1000 Hz 343 m s 343 m s " 68.6 m s # \$ % & ( = 1250 Hz " = v f = 343 m s 1250 Hz = 0.27 m

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Problem 2 (a) E 25 = k e q 25 r 25 2 = 9 " 10 9 Nm 2 C 2 ( ) 25 " 10 # 6 C 0.1 m ( ) 2 = 2.25 " 10 7 E 9 = k e q 9 r 9 2 = 9 " 10 9 Nm 2 C 2 ( ) 9 " 10 # 6 C 0.06 m ( ) 2 = 2.25 " 10 7 tan \$ = 8 cm 6 cm = 4 3 % = 53.1 ° E x = E 25 cos # E 9 = 2.25 " 10 7 N C ( ) cos53.1 ° ( ) # 2.25 " 10 7 = # 9.0 " 10 6 N C E y = # E 25 sin = # 2.25 " 10 7 N C ( ) sin53.1 ° ( ) = # 1.8 " 10 7 N C E = E x 2 + E y 2 = # 9.0 " 10 6 N C ( ) 2 + # 1.8 " 10 7 N C ( ) 2 = 2.01 " 10 7 N C (b) V net = k e q 25 r 25 + q 9 r 9 " # \$ % & = k e 25 q r 25 ( 9 q r 9 " # \$ % & In order for the net electric potential to be zero, the distance to +25q must be greater than the distance to -9q. Thus, it is possible for the net electric potential to be zero in regions (ii) and (iii) (between the charges, and below -9q).
Problem 3 (a) " E = r E # d r A = q in \$ 0 % r E # d r A % = E ( ) 4 & r 2 ( ) q in = V in = Q 4 3 R 3 ( ) * * * + , - - - 4 3 r 3 ( ) * + , - = Q r 3 R 3 ( ) * + , - E ( ) 4 r 2 ( ) = Q 0 r 3 R 3 ( ) * + , - .

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Midterm 2, Physics 6B Summer UCLA - Problem 1(a v vo f"= f...

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